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Wolfram Bugs >1000

Content

  1. Wolfram cannot find SIMPLE solution
  2. Wolfram solutions are wrong
  3. Wolfram cannot solve

There are bugs in many software such as WolframAlpha. Wish wolfram fix the bugs. You can copy equation and paste into MathHand.com, click the ODE button to solve, then click the test button to test its solution.

Wolfram cannot find SIMPLE solution

Its solution is too compliacted, so cannot checked, perhaps the solution is wrong.

first order ODE

  1. y'= cbrt(y)
  2. y'= 2*cbrt(y)
  3. y'= 3*cbrt(y)
  4. y'= (x)*cbrt(y)
  5. y'= (x)^2*cbrt(y)
  6. y'= (x)^3*cbrt(y)
  7. y'= 2*(x)*cbrt(y)
  8. y'= 2*x^2*cbrt(y)
  9. y'= 2*(x)^3*cbrt(y)
  10. y'= (x-1)*cbrt(y)
  11. y'= (x-1)^2*cbrt(y)
  12. y'= (x-1)^3*cbrt(y)
  13. y'= (x)*cbrt(y-1)
  14. y'= (x)^2*cbrt(y-1)
  15. y'= (x)^3*cbrt(y-1)
  16. y'= 2*(x-1)*cbrt(y)
  17. y'= 2*(x-1)^2*cbrt(y)
  18. y'= 2*(x-1)^3*cbrt(y)
  19. y'= 2*(x)*cbrt(y-1)
  20. y'= 2*(x)^2*cbrt(y-1)
  21. y'= 2*(x)^3*cbrt(y-1)

  22. y' *(y^2+x)-2y =0
  23. y' *(y^2+x)-3y =0
  24. y' *(y^2+x)-4y =0
  25. y' *(y^2+x)+3y =0
  26. y' *(y^2+x)+4y =0

  27. y'^2-x*y'-y=0
  28. y'^2-x*y'-2y=0
  29. y'^2-2x*y'-y=0
  30. y'^2-2x*y'-2y=0

  31. y'-x/(y-x-1)=0
  32. y'-(x-1)/(y-x-1)=0
  33. y'-x/(y-x-11)=0
  34. y'-(x-11)/(y-x-11)=0
  35. y'-x/(y-2x-1)=0
  36. y'-(x-11)/(y-x-1)=0
  37. y'-1/(y-x-1)-1=0
  38. y'= -1/(y-x-1)-1

    second order ODE

  39. y''+y' +x*y+x*x+1=0
  40. y''+y' +2x*y+2x*x+1=0

  41. y'' *y'-y=0
  42. y'' *y'-2y=0
  43. y'' *y'-3y=0
  44. y'' *y'-c*y=0

  45. y''-y/(x+1)-1=0
  46. y''-y/(2x+1)-1=0
  47. y''-2y/(2x+1)-1=0

  48. x*y''-y-1-x=0
  49. x*y''-y-1-2x=0
  50. x*y''-y+1-2x=0

  51. x*y''-y-x=0
  52. x*y''-y-2x=0
  53. x*y''-2y-2x=0

  54. y" -(x+y)^2 =0
  55. y" -(x+y)^3 =0
  56. y" -(x+y-1)^2 =0
  57. y" -(x+y-1)^3 =0
  58. y" -(x+y+1)^2 =0
  59. y" -(x+y+1)^3 =0

  60. y''-x^2-2x*y-y^2=0

  61. y' *y'' -x^2-1=0
  62. y' *y'' -x^2-2=0
  63. y' *y'' -x^2-3=0
  64. y' *y'' -x^2+1=0
  65. y' *y'' -x^2+2=0
  66. y' *y'' -x^2+3=0
  67. y' *y'' +x^2-1=0
  68. y' *y'' +x^2-2=0
  69. y' *y'' +x^2-3=0
  70. y' *y'' +x^2+1=0
  71. y' *y'' +x^2+2=0
  72. y' *y'' +x^2+c=0

  73. y''*y'-y^2=0
  74. y''*y'-y^3=0
  75. y''*y'-y^4=0

  76. y''-x*y'-x*y-x=0
  77. y''-x*y'-x*y-2x=0
  78. y''-x*y'-x*y-3x=0
    .......
  79. y''-x*y'-x*y-n*x=0
  80. y''-x*y'-x*y-x^2-x=0
  81. y''-x*y'-x*y-x^3+2=0
  82. y''-x*y'-x*y-x^4-6=0
  83. y''-x*y'-x*y-x^5+24=0
    .......
  84. y''-x*y'-x*y-x^n=0
  85. y''-a*x*y'-b*x*y-c*x^n=0
  86. y''-y'-x*y-x=0
  87. y''-y'-x*y-x^2=0
  88. y''-y'-x*y-x^2-1=0
  89. y''-2*y'-x*y-x^2-2=0
  90. y''-4*y'-x*y-x^2-4=0
  91. y''-y'-x*y-x^3-x^2+1=0
  92. y''-2y'-x*y-x^3-x^2=0
  93. y''-y'-x*y-x^3+2=0
  94. y''-2y'-x*y-x^3+2=0
  95. y''-4y'-x*y-x^3+2=0
  96. y''-6y'-x*y-x^3+2=0
  97. y''-8y'-x*y-x^3+2=0
  98. y''-y'-x*y-x^4+3=0
    .......
  99. y''-y'-x*y-x^n=0
  100. y''-a*y'-b*x*y-c*x^n=0
  101. y''-x*y-x^3+2=0
  102. y''-x*y-x^6+40=0
    .......
  103. y''-x*y-x^n=0
  104. y''-x*y-x^6-x^3+42=0
  105. y''-x^2*y-x^2=0
  106. y''-x^2*y-x^3=0
  107. y''-x^2*y-x^4=0
  108. y''-x^2*y-x^4+2=0
  109. y''-2x^2*y-x^4+1=0
  110. y''-x^3*y-x^3=0
  111. y''-x^3*y-x^4=0
    .......
  112. y''-x^n*y-x^n=0
  113. y''-x^2*y'-x*y-x^2=0
  114. y''-x^2*y'-x*y-2x^2=0
  115. y''-x^2*y'-x*y-3x^2=0
    .......
  116. y''-x^2*y'-x*y-n*x^2=0
  117. y''-x^3*y'-x^2*y-x^3=0
  118. y''-x^3*y'-x^3*y-x^3=0
    .......
  119. y''-x^n*y'-x^n*y-x^n=0
  120. y''-x^2*y'-x*y-x^2=0
  121. y''-x^2*y'-x^2*y-x^3-x^2=0
  122. y''-x^2*y'-x^3*y-x^4-x^2=0
  123. y''-x^3*y'-x*y-x^3-x^2=0
  124. y''-x^3*y'-x^2*y-x^3=0
  125. y''-x^3*y'-x^3*y-x^4-x^3=0
  126. y''-x^3*y'-x^2*y-2x^3=0
  127. y''-x^3*y'-x^2*y-3x^3=0
  128. y''-x^3*y'-x^2*y-4x^3=0
    .......
  129. y''-x^3*y'-x^2*y-n*x^3=0
  130. y''-1/x*y'-x*y-x^2-1/x=0
  131. y''-1/x*y'-x^2*y-x^3-1/x=0
  132. y''-1/x*y'-x^3*y-x^4-1/x=0

  133. y'*y'' -exp(y)=0
  134. y'*y'' -2exp(y)=0
  135. y'*y'' -3exp(y)=0

  136. y'' -y^2 =0
  137. y'' -y^3 =0
  138. y'' -y^2.5 =0
  139. y'' -y^3.5 =0

  140. y''-y^2+y=0
  141. y''-y^2-4y-1=0
  142. y''-y^2-2y-1=0
  143. y''+y^2+2y=0
  144. y''+y^2+2=0

  145. y''-y^3-y=0
  146. y''-y^3+y=0
  147. y''+y^3-y=0
  148. y''+y^3+y=0

    Wolfram solutions are wrong

    first order ODE

  149. y'-y^2-2x^2-1=0
  150. y'-y^2-x^2-3=0
  151. y'-y^2-x^2-x-1=0
  152. y'-y^2-x^2-x-11=0
  153. y'-y^2-x^2-x=0
    ......
  154. y'- y^2 -b *x^2 =0
  155. y'-y^2 -b *x^2-c =0
  156. y'-y^2 -b *x^2-c *x =0
  157. y'-y^2 -b *x^2-c *x-d=0
    Wolfram solution always is 1/(c1-x) for above equations.

  158. y'-2y^2-2x^2-1=0
  159. y'-2y^2-x^2-3x=0
  160. y'-2y^2-x^2-x-1=0
  161. y'-2y^2-x^2-x-11=0
    ......
  162. y'-2 y^2 -b* x^2 =0
  163. y'-2y^2 -b* x^2-c =0
  164. y'-2y^2 -b* x^2-c* x =0
  165. y'-2y^2 -b* x^2-c* x-d =0
    Wolfram solution always is 1/(2 (c1-x)) for above equations.

  166. y'-3y^2-2x^2-1=0
  167. y'-3y^2-x^2-3x=0
  168. y'-3y^2-x^2-x-1=0
  169. y'-3y^2-x^2-x-11=0
    .....
  170. y'-3y^2 -b* x^2 =0
  171. y'-3y^2 -b* x^2-c =0
  172. y'-3y^2 -b* x^2-c* x =0
  173. y'-3y^2 -b* x^2-c* x-d =0
    Wolfram solution always is 1/(3 (c1-x)) for above equations.

  174. y'-a*y^2 -b* x^2 =0
  175. y'-a*y^2 -b* x^2-c* x =0
  176. y'-a*y^2 -b* x^2-d =0
  177. y'-a*y^2 -b* x^2-c* x-d=0
    Wolfram solution always is 1/(a (c1-x)) for above equations.

  178. y'-a*y^2 -y-b* x^2 =0
  179. y'-a*y^2 -y-b* x^2-c *x =0
  180. y'-a*y^2 -y-b* x^2-d =0
  181. y'-a*y^2 -y-b* x^2-c *x-d=0
    Wolfram solution always is 1/(a (c1-x))-1/(2a) for above equations.

  182. y'-a*y^2 -f*y-b*x^2 =0
  183. y'-a*y^2 -f*y-b*x^2-c*x =0
  184. y'-a*y^2 -f*y-b*x^2-d =0
  185. y'-a*y^2 -f*y-b*x^2-c*x-d=0
    Wolfram solution always is 1/(a (c1-x))-f/(2a) for above equations.

    second order ODE

  186. y''-y'*y-x=0
  187. y''-y'*y-2x=0
  188. y''- y* y'-3x=0
    ......
  189. y''- y *y' -c *x=0
    Wolfram solution always is 2/(c1-x) for above equations.

  190. y''+y'*y+x=0
  191. y''+y'*y+2x=0
  192. y''+ y *y'+3x=0
    ......
  193. y''+ y *y' +c *x=0
    Wolfram solution always is 2/(c1+x) for above equations.

  194. y''-2 y*y'-x=0
  195. y''-2 y*y'-2x=0
  196. y''-2 y*y'-3x=0
    ......
  197. y''-2 y*y' -c *x=0
    Wolfram solution always is 1/(c1-x) for above equations.

  198. y''-b*y*y'-x=0
  199. y''-b*y*y'-2x=0
  200. y''-b*y*y'-3x=0
    ......
  201. y''-b*y*y' -c *x=0
    Wolfram solution always is 2/(b (c1-x)) for above equations.

  202. y''+y'*y+x=0
  203. y''+y'*y+2x=0
  204. y''+ y*y'+3x=0
    ......
  205. y''+ y*y' +c*x=0
    Wolfram solution always is 2/(c1+x) for above equations.

  206. y''* y'-y(x)^n=0
  207. y''* y'+y(x)^n=0

    when the minus sign in all above examples changed to the plus sign, wolfram also give wrong result.

    partial differential equation

  208. if adding a term to above equations become the partial differential equations, thier solutions are wrong too.
  209. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-1 == 0
  210. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2 == 0
  211. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-x == 0
  212. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-x-1 == 0
  213. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-x-2 == 0
  214. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2x == 0
  215. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2x-1 == 0
  216. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2x-2 == 0
  217. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-x == 0
  218. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-x-1 == 0
  219. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-x-2 == 0
  220. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-2x == 0
  221. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-2x-1 == 0
  222. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-2x-2 == 0
    ......
    Wolfram solutions always is 1/(c1(x-t)-x)

    Wolfram cannot solve

    Integral

  223. integrate f(x)
  224. integrate(diff(F(x)),x,a,b)

  225. integrate x^x
  226. integrate(x^(-x))
  227. integrate(x^(2x))
  228. integrate(x^(n* x))

  229. integrate x^x/x
  230. integrate x^x/x^2
  231. integrate x^x/exp(x)
  232. integrate(x^(-x)/exp(x))
  233. integrate(x^(2x)/exp(x))
  234. integrate(x^(n* x)/exp(x))

    First order ode

  235. y'=sin(x+y)
  236. y'=sin(x+y+1)
  237. y'=sin(x+y-1)
  238. y'=sin(-x+y)
  239. y'=sin(-x+y+1)
  240. y'=sin(-x+y-1)
  241. y'=sin(y+x)+x
  242. y'=sin(y+x+1)+x
  243. y'=sin(y-x)+x
  244. y'=sin(y-x-1)+x
  245. y'=sin(y-x)-x
  246. y'=sin(y-x-1)-x
  247. y'=sin(y-x^2)+x
  248. y'=sin(y-x^2-1)+x
  249. y'=sin(y-x^2-1)-x

  250. y'= tan(x+y)
  251. y'= cot(x+y)
  252. y'= 1/tan(x+y)
  253. y'= 1/cot(x+y)
  254. y'= 1/csc(y+x)
  255. y'= atan(x+y)
  256. y'= acot(x+y)
  257. y'= asec(x+y)
  258. y'= acsc(x+y)

  259. y'= csch(x+y)
  260. y'= atanh(x+y)
  261. y'= acoth(x+y)
  262. y'= asech(x+y)
  263. y'= acsch(x+y)

  264. y'= asin(y)+cos(x)-x
  265. y'= asin(y-1)+cos(x)-x
  266. y'= asin(y+x^2)+cos(x)-3x
  267. y'= asin(y-1+x^2)+cos(x)-3x
  268. y'= asin(y-x^2/2)+cos(x)
  269. y'= asin(y-1-x^2/2)+cos(x)
  270. y'= asin(y)+cos(x+1)-x-1
  271. y'= asin(y-1)+cos(x+1)-x-1
  272. y'= asin(y+x^2)+cos(x+1)-3x-1
  273. y'= asin(y-1+x^2)+cos(x+1)-3x-1
  274. y'= asin(y)+2cos(2x)-2x
  275. y'= asin(y-1)+2cos(2x)-2x
  276. y'= asin(y-x^2)+2cos(2x)
  277. y'= asin(y-1-x^2)+2cos(2x)
  278. y'= asin(y-x^2)+2cos(2x+1)-1
  279. y'= asin(y-1-x^2)+2cos(2x+1)-1
  280. y'= asin(y-x^2/2)+cos(x+1)-1
  281. y'= asin(y-1-x^2/2)+cos(x+1)-1
  282. y'= 2asin(y)+cos(x)-2x
  283. y'= 2asin(y-1)+cos(x)-2x
  284. y'= 2asin(y+x^2)+cos(x)-5x
  285. y'= 2asin(y-1+x^2)+cos(x)-5x
  286. y'= 2asin(y-x^2/2)+cos(x)-x
  287. y'= 2asin(y-1-x^2/2)+cos(x)-x
  288. y'= 2asin(y)+cos(x+1)-2x-1
  289. y'= 2asin(y-1)+cos(x+1)-2x-1
  290. y'= 2asin(y+x^2)+cos(x+1)-5x-1
  291. y'= 2asin(y-1+x^2)+cos(x+1)-5x-1
  292. y'= 2asin(y)+2cos(2x)-3x
  293. y'= 2asin(y-1)+2cos(2x)-3x
  294. y'= 2asin(y-x^2)+2cos(2x)-x
  295. y'= 2asin(y-1-x^2)+2cos(2x)-x
  296. y'= 2asin(y-x^2)+2cos(2x+1)-1-x
  297. y'= 2asin(y-1-x^2)+2cos(2x+1)-1-x
  298. y'= 2asin(y-x^2/2)+cos(x+1)-1-x
  299. y'= 2asin(y-1-x^2/2)+cos(x+1)-1-x

  300. y'= acos(y)-sin(x)-x
  301. y'= acos(y-1)-sin(x)-x
  302. y'= acos(y+x^2)-sin(x)-3x
  303. y'= acos(y-1+x^2)-sin(x)-3x
  304. y'= acos(y-x^2/2)-sin(x)
  305. y'= acos(y-1-x^2/2)-sin(x)
  306. y'= acos(y)-sin(x+1)-x-1
  307. y'= acos(y-1)-sin(x+1)-x-1
  308. y'= acos(y+x^2)-sin(x+1)-3x-1
  309. y'= acos(y-1+x^2)-sin(x+1)-3x-1
  310. y'= acos(y)-2sin(2x)-2x
  311. y'= acos(y-1)-2sin(2x)-2x
  312. y'= acos(y-x^2)-2sin(2x)
  313. y'= acos(y-1-x^2)-2sin(2x)
  314. y'= acos(y-x^2)-2sin(2x+1)-1
  315. y'= acos(y-1-x^2)-2sin(2x+1)-1
  316. y'= acos(y-x^2/2)-sin(x+1)-1
  317. y'= acos(y-1-x^2/2)-sin(x+1)-1
  318. y'= 2acos(y)-sin(x)-2x
  319. y'= 2acos(y-1)-sin(x)-2x
  320. y'= 2acos(y+x^2)-sin(x)-5x
  321. y'= 2acos(y-1+x^2)-sin(x)-5x
  322. y'= 2acos(y-x^2/2)-sin(x)-x
  323. y'= 2acos(y-1-x^2/2)-sin(x)-x
  324. y'= 2acos(y)-sin(x+1)-2x-1
  325. y'= 2acos(y-1)-sin(x+1)-2x-1
  326. y'= 2acos(y+x^2)-sin(x+1)-4x-1
  327. y'= 2acos(y-1+x^2)-sin(x+1)-4x-1
  328. y'= 2acos(y)-2sin(2x)-3x
  329. y'= 2acos(y-1)-2sin(2x)-3x
  330. y'= 2acos(y-x^2)-2sin(2x)-x
  331. y'= 2acos(y-1-x^2)-2sin(2x)-x
  332. y'= 2acos(y-x^2)-2sin(2x+1)-1-x
  333. y'= 2acos(y-1-x^2)-2sin(2x+1)-1-x
  334. y'= 2acos(y-x^2/2)-sin(x+1)-1-x
  335. y'= 2acos(y-1-x^2/2)-sin(x+1)-1-x

  336. y'= asinh(y)+cosh(x)-x
  337. y'= asinh(y-1)+cosh(x)-x
  338. y'= asinh(y+x^2)+cosh(x)-3x
  339. y'= asinh(y-1+x^2)+cosh(x)-3x
  340. y'= asinh(y-x^2/2)+cosh(x)
  341. y'= asinh(y-1-x^2/2)+cosh(x)
  342. y'= asinh(y)+cosh(x+1)-x-1
  343. y'= asinh(y-1)+cosh(x+1)-x-1
  344. y'= asinh(y+x^2)+cosh(x+1)-3x-1
  345. y'= asinh(y-1+x^2)+cosh(x+1)-3x-1
  346. y'= asinh(y)+2cosh(2x)-2x
  347. y'= asinh(y-1)+2cosh(2x)-2x
  348. y'= asinh(y-x^2)+2cosh(2x)
  349. y'= asinh(y-1-x^2)+2cosh(2x)
  350. y'= asinh(y-x^2)+2cosh(2x+1)-1
  351. y'= asinh(y-1-x^2)+2cosh(2x+1)-1
  352. y'= asinh(y-x^2/2)+cosh(x+1)-1
  353. y'= asinh(y-1-x^2/2)+cosh(x+1)-1
  354. y'= 2asinh(y)+cosh(x)-2x
  355. y'= 2asinh(y-1)+cosh(x)-2x
  356. y'= 2asinh(y+x^2)+cosh(x)-4x
  357. y'= 2asinh(y-1+x^2)+cosh(x)-4x
  358. y'= 2asinh(y-x^2/2)+cosh(x)-x
  359. y'= 2asinh(y-1-x^2/2)+cosh(x)-x
  360. y'= 2asinh(y)+cosh(x+1)-2x-1
  361. y'= 2asinh(y-1)+cosh(x+1)-2x-1
  362. y'= 2asinh(y+x^2)+cosh(x+1)-4x-1
  363. y'= 2asinh(y-1+x^2)+cosh(x+1)-4x-1
  364. y'= 2asinh(y)+2cosh(2x)-3x
  365. y'= 2asinh(y-1)+2cosh(2x)-3x
  366. y'= 2asinh(y-x^2)+2cosh(2x)-x
  367. y'= 2asinh(y-1-x^2)+2cosh(2x)-x
  368. y'= 2asinh(y-x^2)+2cosh(2x+1)-1-x
  369. y'= 2asinh(y-1-x^2)+2cosh(2x+1)-1-x
  370. y'= 2asinh(y-x^2/2)+cosh(x+1)-1-x
  371. y'= 2asinh(y-1-x^2/2)+cosh(x+1)-1-x

  372. y'= acosh(y)-sinh(x)-x
  373. y'= acosh(y-1)-sinh(x)-x
  374. y'= acosh(y+x^2)-sinh(x)-3x
  375. y'= acosh(y-1+x^2)-sinh(x)-3x
  376. y'= acosh(y-x^2/2)-sinh(x)
  377. y'= acosh(y-1-x^2/2)-sinh(x)
  378. y'= acosh(y)-sinh(x+1)-x-1
  379. y'= acosh(y-1)-sinh(x+1)-x-1
  380. y'= acosh(y+x^2)-sinh(x+1)-3x-1
  381. y'= acosh(y-1+x^2)-sinh(x+1)-3x-1
  382. y'= acosh(y)-2sinh(2x)-2x
  383. y'= acosh(y-1)-2sinh(2x)-2x
  384. y'= acosh(y-x^2)-2sinh(2x)
  385. y'= acosh(y-1-x^2)-2sinh(2x)
  386. y'= acosh(y-x^2)-2sinh(2x+1)-1
  387. y'= acosh(y-1-x^2)-2sinh(2x+1)-1
  388. y'= acosh(y-x^2/2)-sinh(x+1)-1
  389. y'= acosh(y-1-x^2/2)-sinh(x+1)-1
  390. y'= 2acosh(y)-sinh(x)-2x
  391. y'= 2acosh(y-1)-sinh(x)-2x
  392. y'= 2acosh(y+x^2)-sinh(x)-4x
  393. y'= 2acosh(y-1+x^2)-sinh(x)-4x
  394. y'= 2acosh(y-x^2/2)-sinh(x)-x
  395. y'= 2acosh(y-1-x^2/2)-sinh(x)-x
  396. y'= 2acosh(y)-sinh(x+1)-2x-1
  397. y'= 2acosh(y-1)-sinh(x+1)-2x-1
  398. y'= 2acosh(y+x^2)-sinh(x+1)-4x-1
  399. y'= 2acosh(y-1+x^2)-sinh(x+1)-4x-1
  400. y'= 2acosh(y)-2sinh(2x)-3x
  401. y'= 2acosh(y-1)-2sinh(2x)-3x
  402. y'= 2acosh(y-x^2)-2sinh(2x)-x
  403. y'= 2acosh(y-1-x^2)-2sinh(2x)-x
  404. y'= 2acosh(y-x^2)-2sinh(2x+1)-1-x
  405. y'= 2acosh(y-1-x^2)-2sinh(2x+1)-1-x
  406. y'= 2acosh(y-x^2/2)-sinh(x+1)-1-x
  407. y'= 2acosh(y-1-x^2/2)-sinh(x+1)-1-x

  408. y'= log(y)+exp(x)-x
  409. y'= log(y-1)+exp(x)-x
  410. y'= log(y+x^2)+exp(x)-3x
  411. y'= log(y-1+x^2)+exp(x)-3x
  412. y'= log(y-x^2/2)+exp(x)
  413. y'= log(y-1-x^2/2)+exp(x)
  414. y'= log(y)+exp(x+1)-x-1
  415. y'= log(y-1)+exp(x+1)-x-1
  416. y'= log(y+x^2)+exp(x+1)-3x-1
  417. y'= log(y-1+x^2)+exp(x+1)-3x-1
  418. y'= log(y-x^2/2)+exp(x+1)-1
  419. y'= log(y-1-x^2/2)+exp(x+1)-1
  420. y'= 2log(y)+exp(x)-2x
  421. y'= 2log(y-1)+exp(x)-2x
  422. y'= 2log(y+x^2)+exp(x)-4x
  423. y'= 2log(y-1+x^2)+exp(x)-4x
  424. y'= 2log(y-x^2/2)+exp(x)-x
  425. y'= 2log(y-1-x^2/2)+exp(x)-x
  426. y'= 2log(y)+exp(x+1)-2x-1
  427. y'= 2log(y-1)+exp(x+1)-2x-1
  428. y'= 2log(y+x^2)+exp(x+1)-4x-1
  429. y'= 2log(y-1+x^2)+exp(x+1)-4x-1
  430. y'= 2log(y-x^2/2)+exp(x+1)-1-x
  431. y'= 2log(y-1-x^2/2)+exp(x+1)-1-x

  432. y'=cbrt(x+y)
  433. y'=cbrt(x+y)-1
  434. y'=cbrt(x+y)+1
  435. y'=cbrt(x+y+1)
  436. y'=cbrt(x+y-1)
  437. y'=cbrt(x+y+1)-1
  438. y'=cbrt(x+y-1)+1
  439. y'=cbrt(-x+y)
  440. y'=cbrt(-x+y+1)
  441. y'=cbrt(-x+y-1)
  442. y'=cbrt(-x+y)-1
  443. y'=cbrt(-x+y+1)-1
  444. y'=cbrt(-x+y-1)-1
  445. y'=cbrt(-x+y)+1
  446. y'=cbrt(-x+y+1)+1
  447. y'=cbrt(-x+y-1)+1
  448. y'=cbrt(y+x)+x
  449. y'=cbrt(y+x+1)+x
  450. y'=cbrt(y-x)+x
  451. y'=cbrt(y-x-1)+x
  452. y'=cbrt(y-x)-x
  453. y'=cbrt(y-x-1)-x
  454. y'=cbrt(y-x^2)+x
  455. y'=cbrt(y-x^2-1)+x
  456. y'=cbrt(y-x^2-1)-x

  457. y'=2cbrt(x+y)
  458. y'=2cbrt(x+y)-1
  459. y'=2cbrt(x+y)+1
  460. y'=2cbrt(x+y+1)
  461. y'=2cbrt(x+y-1)
  462. y'=2cbrt(x+y+1)-1
  463. y'=2cbrt(x+y-1)+1
  464. y'=2cbrt(-x+y)
  465. y'=2cbrt(-x+y+1)
  466. y'=2cbrt(-x+y-1)
  467. y'=2cbrt(-x+y)-1
  468. y'=2cbrt(-x+y+1)-1
  469. y'=2cbrt(-x+y-1)-1
  470. y'=2cbrt(-x+y)+1
  471. y'=2cbrt(-x+y+1)+1
  472. y'=2cbrt(-x+y-1)+1
  473. y'=2cbrt(y+x)+x
  474. y'=2cbrt(y+x+1)+x
  475. y'=2cbrt(y-x)+x
  476. y'=2cbrt(y-x-1)+x
  477. y'=2cbrt(y-x)-x
  478. y'=2cbrt(y-x-1)-x
  479. y'=2cbrt(y-x^2)+x
  480. y'=2cbrt(y-x^2-1)+x
  481. y'=2cbrt(y-x^2-1)-x

  482. y'= cbrt(x*y)
  483. y'= cbrt(2x*y)
  484. y'= 2cbrt(x*y)
  485. y'= 2cbrt(2x*y)
  486. y'= cbrt(x*y)*x
  487. y'= cbrt(2x*y)*x
  488. y'= 2cbrt(x*y)*x
  489. y'= 2cbrt(2x*y)*x
  490. y'= cbrt(x*y)*x^2
  491. y'= cbrt(2x*y)*x^2
  492. y'= 2cbrt(x*y)*x^2
  493. y'= 2cbrt(2x*y)*x^2

  494. y'= (x-1)*cbrt(y-1)
  495. y'= (x-1)^2*cbrt(y-1)
  496. y'= (x-1)^3*cbrt(y-1)
  497. y'= (2*x-1)*cbrt(y-1)
  498. y'= 2*(x-1)^2*cbrt(y-1)
  499. y'= 2*(x-1)^3*cbrt(y-1)
  500. y'= 2*(x)^2*cbrt(y-1)
  501. y'= 2*(x)^3*cbrt(y-1)

  502. y'= (x-1)*cbrt(y-2)
  503. y'= (x-1)^2*cbrt(y-2)
  504. y'= (x-1)^3*cbrt(y-2)
  505. y'= (2*x-1)*cbrt(y-2)
  506. y'= 2*(x-1)^2*cbrt(y-2)
  507. y'= 2*(x-1)^3*cbrt(y-2)

  508. y'=sqrt(x)*cbrt(y)
  509. y'=sqrt(x)*cbrt(y-1)
  510. y'=sqrt(x)*cbrt(y-a)
  511. y'=sqrt(x-1)*cbrt(y)
  512. y'=sqrt(x-1)*cbrt(y-a)
  513. y'=sqrt(x-b)*cbrt(y)
  514. y'=sqrt(x-b)*cbrt(y-a)
  515. y'=1/sqrt(x)*cbrt(y)
  516. y'=1/sqrt(x)*cbrt(y-1)
  517. y'=1/sqrt(x)*cbrt(y-a)
  518. y'=1/sqrt(x-1)*cbrt(y)
  519. y'=1/qrt(x-2)*cbrt(y-a)
  520. y'=1/sqrt(x-b)*cbrt(y)
  521. y'=1/qrt(x-b)*cbrt(y-a)
  522. y'=cbrt(y)*x^n
  523. y'=cbrt(y-1)*x^n
  524. y'=cbrt(y+1)*x^n
  525. y'=2*sqrt(x)*cbrt(y)
  526. y'=2*sqrt(x)*cbrt(y-1)
  527. y'=2*sqrt(x)*cbrt(y-a)
  528. y'=2*sqrt(x-1)*cbrt(y)
  529. y'=2*sqrt(x-1)*cbrt(y-a)
  530. y'=2*sqrt(x-b)*cbrt(y)
  531. y'=2*sqrt(x-b)*cbrt(y-a)
  532. y'=2*1/sqrt(x)*cbrt(y)
  533. y'=2*1/sqrt(x)*cbrt(y-1)
  534. y'=2*1/sqrt(x)*cbrt(y-a)
  535. y'=2*1/sqrt(x-1)*cbrt(y)
  536. y'=2*1/qrt(x-2)*cbrt(y-a)
  537. y'=2*1/sqrt(x-b)*cbrt(y)
  538. y'=2*1/qrt(x-b)*cbrt(y-a)
  539. y'=2*cbrt(y)*x^n
  540. y'=2*cbrt(y-1)*x^n
  541. y'=2*cbrt(y+1)*x^n

  542. y'=sqrt(x)/cbrt(y)
  543. y'=sqrt(x)/cbrt(y-1)
  544. y'=sqrt(x)/cbrt(y-a)
  545. y'=sqrt(x-1)/cbrt(y)
  546. y'=sqrt(x-1)/cbrt(y-a)
  547. y'=sqrt(x-b)/cbrt(y)
  548. y'=sqrt(x-b)/cbrt(y-a)
  549. y'=1/sqrt(x)/cbrt(y)
  550. y'=1/sqrt(x)/cbrt(y-1)
  551. y'=1/sqrt(x)/cbrt(y-a)
  552. y'=1/sqrt(x-1)/cbrt(y)
  553. y'=1/qrt(x-2)/cbrt(y-a)
  554. y'=1/sqrt(x-b)/cbrt(y)
  555. y'=1/qrt(x-b)/cbrt(y-a)
  556. y'=cbrt(y)/x^n
  557. y'=2*sqrt(x)/cbrt(y)
  558. y'=2*sqrt(x)/cbrt(y-1)
  559. y'=2*sqrt(x)/cbrt(y-a)
  560. y'=2*sqrt(x-1)/cbrt(y)
  561. y'=2*sqrt(x-1)/cbrt(y-a)
  562. y'=2*sqrt(x-b)/cbrt(y)
  563. y'=2*sqrt(x-b)/cbrt(y-a)
  564. y'=2*1/sqrt(x)/cbrt(y)
  565. y'=2*1/sqrt(x)/cbrt(y-1)
  566. y'=2*1/sqrt(x)/cbrt(y-a)
  567. y'=2*1/sqrt(x-1)/cbrt(y)
  568. y'=2*1/qrt(x-2)/cbrt(y-a)
  569. y'=2*1/sqrt(x-b)/cbrt(y)
  570. y'=2*1/qrt(x-b)/cbrt(y-a)
  571. y'=2*cbrt(y)/x^n

  572. y'^3=y'+x
  573. y'^3=y'+2x
  574. y'^3=y'+3x
  575. y'^3=2y'+x
  576. y'^3=2y'+2x
  577. y'^3=2y'+3x

  578. y'^4=y'+x
  579. y'^4=y'+2x
  580. y'^4=y'+3x
  581. y'^4=2y'+x
  582. y'^4=2y'+2x
  583. y'^4=2y'+3x

  584. y'^5=y'+x
  585. y'^5=y'+2x
  586. y'^5=y'+3x
  587. y'^5=2y'+x
  588. y'^5=2y'+2x
  589. y'^5=2y'+3x

  590. y'^3+2x*y'-2y-2y^2=0
  591. y'^3+2x*y'-2y-2y^2=1
  592. y'^3+2x*y'-2y-2y^2=2
  593. y'^3+2x*y'-2y-4y^2=0
  594. y'^3+2x*y'-2y-4y^2=1
  595. y'^3+2x*y'-2y-4y^2=2
  596. y'^3+2x*y'-2y-2y^2.5=0
  597. y'^3+2x*y'-2y-2y^2.5=1
  598. y'^3+2x*y'-2y-2y^2.5=2
  599. y'^3+2x*y'-2y-4y^2.5=0
  600. y'^3+2x*y'-2y-4y^2.5=1
  601. y'^3+2x*y'-2y-4y^2.5=2
    ......

    Second order ode

  602. y''= tan(x+y)
  603. y''= cot(x+y)
  604. y''= sec(x+y)
  605. y''= csc(x+y)
  606. y''= tan(x+y+1)
  607. y''= cot(x+y+1)
  608. y''= sec(x+y+1)
  609. y''= csc(x+y+1)
  610. y''= tan(x+y+1)
  611. y''= cot(x+y+1)
  612. y''= sec(x+y+1)
  613. y''= csc(x+y+1)

  614. y''= atan(x+y)
  615. y''= acot(x+y)
  616. y''= asec(x+y)
  617. y''= acsc(x+y)
  618. y''= atan(x+y+1)
  619. y''= acot(x+y+1)
  620. y''= asec(x+y+1)
  621. y''= acsc(x+y+1)
  622. y''= atan(x+y-1)
  623. y''= acot(x+y-1)
  624. y''= asec(x+y-1)
  625. y''= acsc(x+y-1)

  626. y''= tanh(x+y)
  627. y''= coth(x+y)
  628. y''= sech(x+y)
  629. y''= csch(x+y)
  630. y''= tanh(x+y+1)
  631. y''= coth(x+y+1)
  632. y''= sech(x+y+1)
  633. y''= csch(x+y+1)
  634. y''= tanh(x+y-1)
  635. y''= coth(x+y-1)
  636. y''= sech(x+y-1)
  637. y''= csch(x+y-1)

  638. y''= atahn(x+y)
  639. y''= acoth(x+y)
  640. y''= asech(x+y)
  641. y''= acsch(x+y)
  642. y''= atahn(x+y+1)
  643. y''= acoth(x+y+1)
  644. y''= asech(x+y+1)
  645. y''= acsch(x+y+1)
  646. y''= atahn(x+y-1)
  647. y''= acoth(x+y-1)
  648. y''= asech(x+y-1)
  649. y''= acsch(x+y-1)

  650. y'' = exp(-x+y)-1
  651. y'' = exp(-2x+y)-1
  652. y'' = 1/exp(x+y)-1
  653. y'' = 1/exp(2x+y)-1
  654. y'' = exp(x+y)-x
  655. y'' = exp(2x+y)-x
  656. y'' = 1/exp(x+y)-x
  657. y'' = 1/exp(2x+y)-x
  658. y'' = exp(-x*x+y)-2x
  659. y'' = exp(-x*x+y)-2x
  660. y'' = 1/exp(x+y)-2x
  661. y'' = 1/exp(2x*x+y)-2x
  662. y'' = 1/exp(x+y+1)
  663. y'' = 1/exp(2x+y+1)
  664. y'' = 1/exp(x+y+1)-1
  665. y'' = 1/exp(2x+y+1)-1
  666. y'' = exp(-x+y+1)-1
  667. y'' = exp(-2x+y+1)-1
  668. y'' = exp(x+y+1)-x
  669. y'' = exp(2x+y+1)-x
  670. y'' = 1/exp(x+y+1)-x
  671. y'' = 1/exp(2x+y+1)-x
  672. y'' = exp(-x*x+y+1)-2x
  673. y'' = exp(-x*x+y+1)-2x
  674. y'' = 1/exp(x+y+1)-2x
  675. y'' = 1/exp(2x*x+y+1)-2x

  676. y'' = sin(x+y)-1
  677. y'' = sin(-x+y)-1
  678. y'' = cos(x+y)-1
  679. y'' = cos(-x+y)-1
  680. y'' = sin(x+y-1)-1
  681. y'' = sin(-x+y-1)-1
  682. y'' = cos(x+y-1)-1
  683. y'' = cos(-x+y-1)-1
  684. y'' = sinh(x+y)-1
  685. y'' = sinh(-x+y)-1
  686. y'' = cosh(x+y)-1
  687. y'' = cosh(-x+y)-1
  688. y'' = sinh(x+y-1)-1
  689. y'' = sinh(-x+y-1)-1
  690. y'' = cosh(x+y-1)-1
  691. y'' = cosh(-x+y-1)-1

  692. y'' = sqrt(x+y)
  693. y'' = sqrt(2x+y)
  694. y'' = 1/sqrt(x+y)
  695. y'' = 1/sqrt(2x+y)
  696. y'' = cbrt(x+y)
  697. y'' = cbrt(2x+y)
  698. y'' = 1/cbrt(x+y)
  699. y'' = 1/cbrt(2x+y)
  700. y'' = (x+y)^1.5
  701. y'' = (x+y)^2.5
  702. y'' = (x+y)^3.5
  703. y'' = 1/(x+y)^1.5
  704. y'' = 1/(x+y)^2.5
  705. y'' = 1/(x+y)^3.5
  706. y'' = 1/(x+y)^4
  707. y'' = sqrt(x+y+1)
  708. y'' = sqrt(2x+y+1)
  709. y'' = 1/sqrt(x+y+1)
  710. y'' = 1/sqrt(2x+y+1)
  711. y'' = cbrt(x+y+1)
  712. y'' = cbrt(2x+y+1)
  713. y'' = 1/cbrt(x+y+1)
  714. y'' = 1/cbrt(2x+y+1)
  715. y'' = (x+y+1)^1.5
  716. y'' = (x+y+1)^2.5
  717. y'' = (x+y+1)^3.5
  718. y'' = 1/(x+y+1)^1.5
  719. y'' = 1/(x+y+1)^2.5
  720. y'' = 1/(x+y+1)^3.5
  721. y'' = 1/(x+y+1)^4

  722. y'' = x*sqrt(x+y+1)
  723. y'' = x*sqrt(2x+y+1)
  724. y'' = x/sqrt(x+y+1)
  725. y'' = x/sqrt(2x+y+1)
  726. y'' = x*cbrt(x+y+1)
  727. y'' = x*cbrt(2x+y+1)
  728. y'' = x/cbrt(x+y+1)
  729. y'' = x/cbrt(2x+y+1)
  730. y'' = x*(x+y+1)^0.5
  731. y'' = x*(x+y+1)^1.5
  732. y'' = x*(x+y+1)^2.5
  733. y'' = x*(x+y+1)^3.5
  734. y'' = x*(x+y+1)^4
  735. y'' = x*(x+y+1)^0.5
  736. y'' = x/(x+y+1)^1.5
  737. y'' = x/(x+y+1)^2.5
  738. y'' = x/(x+y+1)^3.5
  739. y'' = x/(x+y+1)^4
    ......

  740. y'' = (x-1)*sqrt(x+y+1)
  741. y'' = (x-1)*sqrt(2x+y+1)
  742. y'' = (x-1)/sqrt(x+y+1)
  743. y'' = (x-1)/sqrt(2x+y+1)
  744. y'' = (x-1)*cbrt(x+y+1)
  745. y'' = (x-1)*cbrt(2x+y+1)
  746. y'' = (x-1)/cbrt(x+y+1)
  747. y'' = (x-1)/cbrt(2x+y+1)
  748. y'' = (x-1)*(x+y+1)^0.5
  749. y'' = (x-1)*(x+y+1)^1.5
  750. y'' = (x-1)*(x+y+1)^2.5
  751. y'' = (x-1)*(x+y+1)^3.5
  752. y'' = (x-1)/(x+y+1)^1.5
  753. y'' = (x-1)/(x+y+1)^2.5
  754. y'' = (x-1)/(x+y+1)^3.5
  755. y'' = (x-1)/(x+y+1)^4

  756. y'' = (x^2-1)*sqrt(x+y+1)
  757. y'' = (x^2-1)*sqrt(2x+y+1)
  758. y'' = (x^2-1)/sqrt(x+y+1)
  759. y'' = (x^2-1)/sqrt(2x+y+1)
  760. y'' = (x^2-1)*cbrt(x+y+1)
  761. y'' = (x^2-1)*cbrt(2x+y+1)
  762. y'' = (x^2-1)/cbrt(x+y+1)
  763. y'' = (x^2-1)/cbrt(2x+y+1)
  764. y'' = (x^2-1)*(x+y+1)^0.5
  765. y'' = (x^2-1)*(x+y+1)^2
  766. y'' = (x^2-1)*(x+y+1)^3
  767. y'' = (x^2-1)*(x+y+1)^4
  768. y'' = (x^2-1)/(x+y+1)^0.5
  769. y'' = (x^2-1)/(x+y+1)^2
  770. y'' = (x^2-1)/(x+y+1)^3
  771. y'' = (x^2-1)/(x+y+1)^4

  772. y'' = (x^2-4x+4)*sqrt(x+y+1)
  773. y'' = (x^2-4x+4)*sqrt(2x+y+1)
  774. y'' = (x^2-4x+4)/sqrt(x+y+1)
  775. y'' = (x^2-4x+4)/sqrt(2x+y+1)
  776. y'' = (x^2-4x+4)*cbrt(x+y+1)
  777. y'' = (x^2-4x+4)*cbrt(2x+y+1)
  778. y'' = (x^2-4x+4)/cbrt(x+y+1)
  779. y'' = (x^2-4x+4)/cbrt(2x+y+1)
  780. y'' = (x^2-4x+4)*(x+y+1)^0.5
  781. y'' = (x^2-4x+4)*(x+y+1)^1.5
  782. y'' = (x^2-4x+4)*(x+y+1)^2.5
  783. y'' = (x^2-4x+4)*(x+y+1)^3.5
  784. y'' = (x^2-4x+4)/(x+y+1)^1.5
  785. y'' = (x^2-4x+4)/(x+y+1)^2.5
  786. y'' = (x^2-4x+4)/(x+y+1)^3.5
  787. y'' = (x^2-4x+4)/(x+y+1)^4

  788. y'' -y^4 =0
  789. y'' -y^5 =0
  790. y'' -y^6 =0
  791. y'' -1/y^4 =0
  792. y'' -1/y^5 =0
  793. y'' -1/y^6 =0

  794. y''*y' -y^5 =0
  795. y''*y' -3y^6 =0
  796. y''*y' -4y^n =0

  797. y'' -x* y * y' =0
  798. y'' -x^2* y * y' =0
  799. y'' -x^3* y * y' =0
  800. y'' -x^n* y * y' =0

  801. y'' -y^3 *x =0
  802. y'' -y^4 *x =0
  803. y'' -y^5 *x =0
  804. y'' -y^n *x =0

  805. y'' -2y^4 *x =0
  806. y'' -2y^5 *x =0
  807. y'' -b*y^n *x =0

  808. y'' -sqrt(x) *y* y' =0
  809. y'' -2sqrt(x) *y* y' =0

  810. y'' -x^2 *y* y'=0
  811. y''- x^2*y *y' =0
  812. y''- x^3*y * y''' =0
  813. y''- x^4*y *y''' =0

  814. y'' +x*y*y' -x^2=0
  815. y'' -x*y*y' +x^2=0

  816. y'' - y^2 -x^2=0
  817. y''- 2y^2 -8x^2=0
  818. y'' +b*y^2 +c x^2=0

  819. y'' y' -exp(x)*y^2=0
  820. y''-exp(x)*y^2=0

  821. exp(x)*y''- y^2=0
  822. (x)*y''- y^2=0
  823. (x) *y'' - y^3=0
  824. (x^2)*y''- y^3=0
  825. (x^n)*y''- y^2=0
  826. exp(x)*y''- y*y'=0
  827. exp(x)*y''- y*y'=0
  828. y''-exp(x)*y*y'=0
  829. y''-exp(x)*y*y'=0
  830. y'' -exp(x)*y'=0
  831. y'*y'' -x*y =0
  832. y'*y'' -x^2*y^2 =0
  833. y'*y'' -x^m*y^n =0

  834. y^2*y'' -x =0
  835. y^2*y'' -a*x^2 =0
  836. y^2*y'' -x^2=0
  837. y^2*y'' -x^3=0
  838. y^2*y'' -x^n=0
  839. y^2*y'' -(1+x)^2=0
  840. y^2*y'' -(2+x)^3=0
  841. y^2*y'' -(3+x)^n=0
  842. exp(x)*y'' - y*y'=0
  843. 2exp(x)*y'' - y*y'=0

  844. y^3*y'' -x=0
  845. y^3*y'' -a*x^2 =0
  846. y^3*y'' -x^2=0
  847. y^3*y'' -x^3=0
  848. y^3*y'' -x^n=0

  849. y*y'*y'' =x
  850. y*y'*y'' =x^2
  851. y*y'*y'' =x^3
  852. y*y'*y'' =x^n

  853. y'' = exp(x)*y^2
  854. y'' = exp(x-1)*y^2
  855. y'' = exp(x-c)*y^2

  856. y'' = exp(x)*y^3
  857. y'' = exp(x-1)*y^3
  858. y'' = exp(x-c)*y^3

  859. y'' = exp(x)*y^n
  860. y'' = exp(x-1)*y^n
  861. y'' = exp(x-c)*y^n

  862. y'' = exp(y-x-c)
  863. y'' = exp(y)*x
  864. y'' = exp(y-x)*x
  865. y'' = exp(y-x-c)*x
  866. y'' = exp(y-x-1)*x^2
  867. y'' = exp(y-2x-c)*x^3
  868. y'' = exp(y-3x-c)*x^4
  869. y'' = exp(y-x-c)*x^5
  870. y'' = exp(y)*x^n
  871. y'' = exp(y-x)*x^n
  872. y'' = exp(y-x-c)*x^n

  873. y'' = exp(y-x^2-1)+2
  874. y'' = exp(y-x^2-x-2)+2
  875. y'' = exp(y-x^3-x-3)+6x
  876. y'' = exp(y-x^2-c)+2
  877. y'' = exp(y-x^2-x-c)+2
  878. y'' = exp(y-x^3-x-c)+6x

  879. y^2 *y''-x^2-4x-4=0
  880. y^2 *y''-x^2-4x=0
  881. y^2 *y''-x^2-4=0

  882. 1/y^2 *y''-x^2-4x-4=0
  883. 1/y^2 *y''-x^2-4x=0
  884. 1/y^2 *y''-x^2-4=0

  885. y^4 *y''-x^2-4x-4=0
  886. y^4 *y''-x^2-4x=0
  887. y^4 *y''-x^2-4=0

  888. 1/y^4 *y''-x^2-4x-4=0
  889. 1/y^4 *y''-x^2-4x=0
  890. 1/y^4 *y''-x^2-4=0

  891. y^(1/2) *y''-x^2-4x-4=0
  892. y^(1/2) *y''-x^2-4x=0
  893. y^(1/2) *y''-x^2-4=0

  894. 1/y^(1/2) *y''-x^2-4x-4=0
  895. 1/y^(1/2) *y''-x^2-4x=0
  896. 1/y^(1/2) *y''-x^2-4=0

  897. y*y'' -2x^2-x-1=0
  898. y*y'' -x^2=0
  899. y*y'' -x^3=0
  900. y*y'' -x^n=0
  901. y*y'' -(1+x)*(x-2)=0
  902. y*y'' -(1+x)*(2x+1)=0
  903. y*y'' -(1+x)^2=0
  904. y*y'' -(2+x)^3=0
  905. y*y'' -(3+x)^n=0
  906. y*y'' -2x^2-b* x-c =0
  907. y* y''-x^3-3x^2-3x-1=0
  908. y* y''-3x^2-3x-1=0
  909. y* y''-3x-1=0
  910. y* y''-x^2-b*x-c =0
  911. y* y''-x^2-b*x =0
  912. y* y''-x^2-c =0
  913. y* y''-a*x^2-b*x-c =0
  914. y* y''-a*x^2-b*x =0
  915. y* y''-a*x^2-c =0
  916. y* y''-x-c =0
  917. y* y''-b*x-c =0

  918. y'' *(y-1)-x^2-4x-4 =0
  919. y'' *(y-1)-4x^2-4x-1 =0
  920. y'' *(y-1)-x^2- 4 =0
  921. y'' *(2y-1)-x^2-4x-4 =0
  922. y'' *(2y-1)-4x^2-4x-1 =0
  923. y'' *(2y-1)-x^2- 4 =0
  924. y'' *(2y-1)-4x-4 =0
  925. y'' *(2y-1)-x^2 =0
  926. y'' *(2y-1)-x =0
  927. y'' *(y-x-1)-x^2-4x-4 =0
  928. y'' *(y-x-1)-4x^2-4x-1 =0
  929. y'' *(y-x-1)-x^2- 4 =0
  930. y'' *(y-2x-1)-x^2-4x-4 =0
  931. y'' *(y-2x-1)-4x^2-4x-1 =0
  932. y'' *(y-2x-1)-x^2- 4 =0

  933. y*y'' -x -y'*x =0
  934. y*y'' -4x -y'*x =0
  935. y*y'' -x -2y'*x =0
  936. y*y'' -4x -2y'*x =0

  937. y''^2+x^2*y''-2y=0
  938. y''^2+x^2*y''-2y=1
  939. y''^2+x^2*y''-2y=2
  940. y''^2+2x^2*y''-4y=0
  941. y''^2+2x^2*y''-4y=1
  942. y''^2+2x^2*y''-4y=2

    Third order ode

    It cannot seem to solve the high order nonlinear ODE.

  943. y'''= y''^2-y'*y
  944. y'''= 2y''^2-2y'*y
  945. y'''= 3y''^2-3y'*y
  946. y'''= -y''^2+y'*y
  947. y'''= -2y''^2+2y'*y
  948. y'''= -3y''^2+3y'*y

  949. y''' -y^2 =0
  950. y''' -y^3 =0
  951. y''' -y^4 =0
  952. y''' -y^5 =0
  953. y''' -y^n =0

  954. y''' -sqrt(y) =0
  955. y''' -cbrt(y) =0
  956. y''' = exp(y)
  957. y''' -sqrt(x+y) =0
  958. y''' -cbrt(x+y) =0
  959. y''' = exp(x+y)
  960. y''' -sqrt(x^2+y) =0
  961. y''' -cbrt(x^2+y) =0
  962. y''' = exp(x^2+y)
  963. y''' -sqrt(x^2+x+y) =0
  964. y''' -cbrt(x^2+x+y) =0
  965. y''' = exp(x^2+x+y)
  966. y''' -sqrt(y+1) =0
  967. y''' -cbrt(y+1) =0
  968. y''' = exp(y+1)
  969. y''' -sqrt(x+y+1) =0
  970. y''' -cbrt(x+y+1) =0
  971. y''' = exp(x+y+1)
  972. y''' -sqrt(x^2+y+1) =0
  973. y''' -cbrt(x^2+y+1) =0
  974. y''' = exp(x^2+y+1)
  975. y''' -sqrt(x^2+x+y+1) =0
  976. y''' -cbrt(x^2+x+y+1) =0
  977. y''' = exp(x^2+x+y+1)

  978. y''' -2y^2 =0
  979. y''' -3y^3 =0
  980. y''' -4y^4 =0
  981. y''' -5y^5 =0
  982. y''' -a*y^n =0

  983. y''' -1/y =0
  984. y''' -1/y^2 =0
  985. y''' -1/y^3 =0
  986. y''' -1/y^4 =0
  987. y''' -1/y^5 =0
  988. y''' -1/sqrt(y) =0
  989. y''' -1/cbrt(y) =0
  990. y''' = 1/exp(y)

  991. y''' -2y^2 *x =0
  992. y''' -3y^3 *x =0
  993. y''' -4y^4 *x =0
  994. y''' -5y^5 *x =0
  995. y''' -y^n *x =0

  996. y''' -y^m *x =0

  997. y''' -2y^2 *x^2 =0
  998. y''' -2y^3 *x^2 =0
  999. y''' -2y^4 *x^2 =0
  1000. y''' -y^5 *x^2 =0
  1001. y''' -b*y^n *x^2 =0

  1002. y'''-y^2-x^2 =0
  1003. y'''-y^2-4x^2 =0
  1004. y'''-y^2-x^4 =0
  1005. y'''-y^2-4x^4 =0
  1006. y'''-x*y^2-x^3 =0
  1007. y'''-x^2*y^2-x^4 =0
  1008. y'''-x*y^2-x^2* y=0
  1009. y'''-x^2*y^2-x^3* y =0

  1010. y''' -b*y^m *x^n =0

  1011. x*y''' -y* y' =0
  1012. x^2*y''' -y* y' =0

  1013. y''' -x *y* y' =0
  1014. y''' -2x *y* y' =0
  1015. y'''' -x *y* y'' =0
  1016. y''' -x *y* y' =0

  1017. y''' -x^2 *y* y'' =0
  1018. y''' -x^3 *y* y'' =0
  1019. y''' -x^2 *y* y'' =0

  1020. y''' -sqrt(x) *y* y' =0
  1021. y''' -sqrt(x) *y* y' =0

  1022. y''' -x^2*y * y''' =0
  1023. y''' -x^a *y* y''=0

  1024. y'''-x^2*y'-x*y-x^2=0
  1025. y'''-x^2*y'-x*y-2x^2=0
  1026. y'''-x^2*y'-x*y-3x^2=0
  1027. y'''-x^2*y'-x*y-c*x^2=0

  1028. y'''-x^3*y'-x^2*y-x^3=0
  1029. y'''-x^3*y'-x^2*y-2*x^3=0
  1030. y'''-x^3*y'-x^2*y-3*x^3=0
  1031. y'''-x^3*y'-x^2*y-c*x^3=0

  1032. y'''-x*y'-x*y-x =0
  1033. y'''-x*y'-x*y-x^2=0
  1034. y'''-x*y'-x*y-x^3=0
  1035. y''' -x*y'-x*y-x^n=0

  1036. y''' -exp(x)*y^2=0
  1037. y''' -exp(x)*y^3=0
  1038. y''' -exp(x)*y^n=0

  1039. exp(x)*y''- y * y''' =0
  1040. exp(x) *y''' - y^2=0
  1041. exp(x)* y''' - y^3=0
  1042. exp(x)* y''' - y^n=0

  1043. (x) *y''' - y^2=0
  1044. (x) * y''' - y^2=0
  1045. (x) * y''' - y^3=0
  1046. (x) * y''' - y^p=0

  1047. (x^2) *y''' - y^2=0
  1048. (x^2) *y''' - y^3=0
  1049. (x^n) *y''' - y^2=0
  1050. (x^n) *y''' - y^3=0
  1051. (x^n)* y''' - y^p=0

  1052. y''' -exp(x)*y*y'=0
  1053. y''' +exp(x)*y*y'=0

  1054. y''' - y*y'=0
  1055. exp(x) * y''' - y*y'=0

  1056. y''' -exp(x) *y' =0
  1057. y''' -exp(x)*y * y'' =0
  1058. y''' -exp(x)*y * y' =0

  1059. exp(x)*y''' - y * y'' =0
  1060. exp(x) * y''' - y* y''=0

  1061. 3exp(x)*y''- y * y''' =0
  1062. 4exp(x)*y''' - y * y'' =0
  1063. a*exp(x) * y''' - y * y'' =0

  1064. y'*y''' -x^2 =0
  1065. y'*y''' -x^3 =0
  1066. y'*y''' -x^4 =0
  1067. y'*y''' -x^m =0
  1068. y'*y''' -x-c =0
  1069. y'*y''' -x^2 -b*x=0
  1070. y'*y''' -a*x^2 -b*x-c=0
  1071. y'*y''' -x*y =0
  1072. y'*y''' -x^2*y^2 =0
  1073. y'*y''' -x^m*y^n =0

  1074. y^2*y''' -x^2=0
  1075. y^2*y''' -x^3=0
  1076. y^2*y''' -x^n=0

  1077. y^2*y''' -(1+x)^2=0
  1078. y^2*y''' -(2+x)^3=0
  1079. y^2*y''' -(3+x)^n=0

  1080. y^3*y''' -x^2=0
  1081. y^3*y''' -x^3=0
  1082. y^3*y''' -x^n=0

  1083. y^m*y'' -x^n =0
  1084. y^m*y''' -x^n =0

  1085. y*y'*y''' =x
  1086. y*y'*y''' =x^2
  1087. y*y'*y''' =x^3
  1088. y*y'*y''' =x^n

  1089. y*y''*y''' =x
  1090. y*y''*y''' =x^2
  1091. y*y''*y''' =x^3
  1092. y*y''*y''' =x^n

  1093. y'*y''*y''' =x
  1094. y'*y''*y''' =x^2
  1095. y'*y''*y''' =x^3
  1096. y'*y''*y''' =x^n

  1097. y''' = exp(x)*y^2
  1098. y''' = exp(x-1)*y^2
  1099. y''' = exp(x-2)*y^2
  1100. y''' = exp(x-3)*y^2
  1101. y''' = exp(x-c)*y^2

  1102. y''' = exp(x)*y^3
  1103. y''' = exp(x-1)*y^3
  1104. y''' = exp(2x-2)*y^3
  1105. y''' = exp(x-3)*y^3
  1106. y''' = exp(2x-c)*y^3
  1107. y''' = exp(x)*y^m
  1108. y''' = exp(a*x-b)*y^m

  1109. y''' = exp(y-3x^2-3x-1)
  1110. y''' = sqrt(y-3x^2-3x-1)
  1111. y''' = cbrt(y-3x^2-3x-1)
  1112. y''' = sin(y-3x^2-3x-1)
  1113. y''' = sinh(y-3x^2-3x-1)

  1114. y''' = exp(y-x^3-3x^2-3x-1)+6
  1115. y''' = sqrt(y-x^3-3x^2-3x-1)+6
  1116. y''' = cbrt(y-x^3-3x^2-3x-1)+6
  1117. y''' = sin(y-x^3-3x^2-3x-1)+6
  1118. y''' = tan(y-x^3-3x^2-3x-1)+6
  1119. y''' = sinh(y-x^3-3x^2-3x-1)+6
  1120. y''' = tanh(y-x^3-3x^2-3x-1)+6

  1121. y'*y''' = exp(x)
  1122. y'*y''' = exp(x-1)
  1123. y'*y''' = exp(x-2)
  1124. y'*y''' = exp(x-3)
  1125. y'*y''' = exp(x-c)

  1126. y'*y''*y''' = exp(x)
  1127. y'*y'' = exp(x)*y'''
  1128. y''*y''' = exp(x)*y'
  1129. y'*y''' = exp(x)*y''
  1130. y''' = exp(x) *y' *y''
  1131. y''' = exp(x) *y' *y
  1132. y''' = exp(x) *y'' *y
  1133. y''' = exp(x+y)
  1134. y''' = exp(x)*y'
  1135. y''' = exp(x)*y''

  1136. y''' = exp(y)
  1137. y''' = exp(y-1)
  1138. y''' = 2exp(y)
  1139. y''' = 3exp(y-1)
  1140. y''' = y' exp(y)
  1141. y''' = y'' exp(y)
  1142. y''' y' = exp(y)
  1143. y''' y''= exp(y)
  1144. y''' = exp(y)
  1145. y''' = a *exp(y+c)
  1146. y''' = y' *exp(y+c)
  1147. y'''* y'' = exp(y+c)

  1148. y*y''' -x^2=0
  1149. y*y''' -x^3=0
  1150. y*y''' -x^n=0
  1151. y*y''' -(1+x)*(x+2)*(x+3)=0
  1152. y*y''' -(1+x)*(2x+1)*(3x+1)=0
  1153. y*y''' -(1+x)^2=0
  1154. y*y''' -(2+x)^3=0
  1155. y*y''' -(3+x)^n=0
  1156. y*y''' -3x^3-b*x^2-c*x-d =0
  1157. y*y'''-6x^3-2x^2-2x-1 =0
  1158. y*y'''-2x^3-2x^2-2x =0
  1159. y*y'''-x^3-2x^2-2x-1 =0
  1160. y*y'''-x^3-b*x^2-c*x-d =0
  1161. y*y'''-x^3-b*x^2-c*x =0
  1162. y*y'''-x^3-b*x^2 =0
  1163. y*y'''-x^3-b*x^2-d =0
  1164. y*y'''-x^3-c*x-d =0
  1165. y*y'''-a*x^3-b*x^2-c*x-d =0
  1166. y*y'''-a*x^3-b*x^2-c*x =0
  1167. y*y'''-a*x^3-b*x^2 =0
  1168. y*y'''-a*x^3-b*x^2-d =0
  1169. y*y'''-a*x^3-c*x-d =0
  1170. y*y'''- x^2 =0
  1171. y*y'''- 2x^2 =0
  1172. y*y'''- 3x^2 =0
  1173. y*y'''- a*x^2 =0

  1174. y* y'''-x^n =0
  1175. y* y'''-2x^n =0
  1176. y* y'''-3x^n =0
  1177. y* y'''-a*x^n-b*x-c =0

  1178. y*y'''-y^3-x^2 =0
  1179. y*y'''-y^3-4x^2 =0
  1180. y*y'''-y^3-x^4 =0
  1181. y*y'''-y^3-4x^4 =0
  1182. y*y'''-x*y^3-x^3 =0
  1183. y*y'''-x^2*y^3-x^2 =0
  1184. y*y'''-x*y^3-x^4=0
  1185. y*y'''-x^2*y^3-x^6=0
  1186. y*y'''-x*y^3-4x^3 =0
  1187. y*y'''-x^2*y^3-4x^2 =0
  1188. y*y'''-x*y^3-4x^4=0
  1189. y*y'''-x^2*y^3-4x^6=0

  1190. y*y''' -x -y' =0
  1191. y*y''' -2x -y' =0
  1192. y*y''' -x -2y' =0
  1193. y*y''' -4x -2y' =0

  1194. y*y''' -x -y''*x =0
  1195. y*y''' -2x -y''*x =0
  1196. y*y''' -x -2y''*x =0
  1197. y*y''' -4x -2y''*x =0

  1198. y'''+y* y''-3x^2-3x-1=0
  1199. y'''+y* y''-3x^2-1=0
  1200. y'''+y* y''-x^2-b*x-c =0
  1201. y'''+y* y''-x^2-b*x =0
  1202. y'''+y* y''-x^2-c =0
  1203. y'''+y* y''-a*x^2-b*x-c =0
  1204. y'''+y* y''-a*x^2-b*x =0
  1205. y'''+y* y''-a*x^2-c =0

    ......

    high order >3 ODE

    if the order of all above equations changed to high order, wolfram cannot solve too.
  1206. y*y'''' -x^2=0
  1207. y*y'''' -x^3=0
  1208. y*y'''' -x^n=0
  1209. y*y'''' -(1+x)*(x+2)*(x+3)*(x+4)=0
  1210. y*y'''' -(1+x)*(2x+1)*(x+2)*(x+3)=0
  1211. y*y'''' -(1+x)^2=0
  1212. y*y'''' -(2+x)^3=0
  1213. y*y'''' -(3+x)^n=0
  1214. y*y'''' -a*x^4-b*x^3-c*x^2-d*x-f =0

  1215. y'*y'''' -x^2 =0
  1216. y'*y'''' -x^3 =0
  1217. y'*y'''' -x^4 =0
  1218. y'*y'''' -x^m =0
  1219. y'*y'''' -x^2 -4x-4=0
  1220. y'*y'''' -x^3 -b*x^2-c*x=0
  1221. y'*y'''' -a*x^3 -b*x^2-c*x+f=0
  1222. y'*y'''' -x*y =0
  1223. y'*y'''' -x^2*y^2 =0
  1224. y'*y'''' -x^m*y^n =0

  1225. y''*y'''' -x^2 -b*x-c=0
  1226. y''*y'''' -x^2-c*x=0
  1227. y''*y'''' -x-c =0
  1228. y''*y'''' -b*x^2-c*x+f=0
  1229. y''*y'''' -x^2*y^2 =0
  1230. y''*y'''' -x^m*y^n =0

    ... ...

    fractional order

  1231. if the order of all these equations changed to fractional order, wolfram cannot solve too.
  1232. It cannot solve fractional calculus
  1233. fractional order differential equations,
  1234. pi-order differential equations,
  1235. negative order differential equations,
  1236. complex order differential equations,
  1237. variable order differential equations
  1238. fractional order integral equations,
  1239. double integral equations,
  1240. fractional order partial integral equations,
  1241. complex order partial differential equations,
  1242. Equation of mixed Fractional differential and integral orders
  1243. Equation of mixed Fractional partial differential and integral orders

    partial differential equation

  1244. if adding a term to above equations become the partial differential equations, wolfram has the same problem.
  1245. high order partial differential equations
  1246. fractional order partial differential equations,
mathHand.com can solve all above and below examples. wolfram also cannot solve or cannot find simple solution in over 110 examples as follows: 
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