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Wolfram Bugs

Content

  • Wolfram solutions are wrong
  • Wolfram cannot find SIMPLE solution
  • 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 solutions are wrong

      first order ODE

    1. y'-y^2-2x^2-1=0
    2. y'-y^2-x^2-3=0
    3. y'-y^x-x^2-x-1=0
    4. y'-y^x-x^2-x=0
    5. ......
    6. y'- y^2 -b *x^2 =0
    7. y'-y^2 -b *x^2-c =0
    8. y'-y^2 -b *x^2-c *x =0
    9. y'-y^2 -b *x^2-c *x-d=0
      Wolfram solution always is 1/(c1-x) for above equations.

    10. y'-2y^2-2x^2-1=0
    11. y'-2y^2-x^2-3x=0
    12. y'-2y^2-x^2-x-1=0
    13. ......
    14. y'-2 y^2 -b* x^2 =0
    15. y'-2y^2 -b* x^2-c =0
    16. y'-2y^2 -b* x^2-c* x =0
      Wolfram solution always is 1/(2 (c1-x)) for above equations.

    17. y'-a*y^2 -b* x^2 =0
    18. y'-a*y^2 -b* x^2-c* x =0
    19. y'-a*y^2 -b* x^2-d =0
    20. y'-a*y^2 -b* x^2-c* x-d=0
      Wolfram solution always is 1/(a (c1-x)) for above equations.

    21. y'-a*y^2 -y-b* x^2 =0
    22. y'-a*y^2 -y-b* x^2-c *x =0
    23. y'-a*y^2 -y-b* x^2-d =0
    24. 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.

    25. y'-a*y^2 -f*y-b*x^2 =0
    26. y'-a*y^2 -f*y-b*x^2-c*x =0
    27. y'-a*y^2 -f*y-b*x^2-d =0
    28. 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

    29. y''-y'*y-x=0
    30. y''-y'*y-2x=0
    31. y''- y* y'-3x=0
    32. ......
    33. y''- y *y' -c *x=0
      Wolfram solution always is 2/(c1-x) for above equations.

    34. y''+y'*y+x=0
    35. y''+y'*y+2x=0
    36. y''+ y *y'+3x=0
    37. ......
    38. y''+ y *y' +c *x=0
      Wolfram solution always is 2/(c1+x) for above equations.

    39. y''-2 y*y'-x=0
    40. y''-2 y*y'-2x=0
    41. y''-2 y*y'-3x=0
    42. ......
    43. y''-2 y*y' -c *x=0
      Wolfram solution always is 1/(c1-x) for above equations.

    44. y''-b*y*y'-x=0
    45. y''-b*y*y'-2x=0
    46. y''-b*y*y'-3x=0
    47. ......
    48. y''-b*y*y' -c *x=0
      Wolfram solution always is 2/(b (c1-x)) for above equations.

    49. y''+y'*y+x=0
    50. y''+y'*y+2x=0
    51. y''+ y*y'+3x=0
    52. ......
    53. y''+ y*y' +c*x=0
      Wolfram solution always is 2/(c1+x) for above equations.

    54. y''* y'-y(x)^n=0
    55. y''* y'+y(x)^n=0

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

      Wolfram cannot find SIMPLE solution

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

      first order ODE

    56. y'= (x)*cbrt(y)
    57. y'=(x)^2*cbrt(y)
    58. y'=(x)^3*cbrt(y)
    59. y' *(y^2+x)-2y =0
    60. y' *(y^2+x)-3y =0
    61. y' *(y^2+x)-4y =0
    62. y' *(y^2+x)+3y =0
    63. y' *(y^2+x)+4y =0

    64. y'-1/(y-x-1)-1=0
    65. y'+1/(y-x-1)-1=0

      second order ODE

    66. y''+y' +x*y+x*x+1=0
    67. y''+y' +2x*y+2x*x+1=0

    68. y'' *y'-y=0
    69. y'' *y'-2y=0
    70. y'' *y'-3y=0
    71. y'' *y'-c*y=0

    72. y" -(x+y)^2 =0
    73. y" -(x+y)^3 =0

    74. y' *y'' -x^2-1=0
    75. y' *y'' -x^2-2=0
    76. y' *y'' -x^2-3=0
    77. y' *y'' -x^2+1=0
    78. y' *y'' -x^2+2=0
    79. y' *y'' -x^2+3=0
    80. y' *y'' +x^2-1=0
    81. y' *y'' +x^2-2=0
    82. y' *y'' +x^2-3=0
    83. y' *y'' +x^2+1=0
    84. y' *y'' +x^2+2=0
    85. y' *y'' +x^2+c=0

    86. y''*y'-y^2=0
    87. y''*y'-y^3=0
    88. y''*y'-y^4=0

    89. y''-x*y'-x*y-x=0
    90. y''-x*y'-x*y-2x=0
    91. y''-x*y'-x*y-3x=0
    92. .......
    93. y''-x*y'-x*y-n*x=0
    94. y''-x*y'-x*y-x^2-x=0
    95. y''-x*y'-x*y-x^3+2=0
    96. y''-x*y'-x*y-x^4-6=0
    97. y''-x*y'-x*y-x^5+24=0
    98. .......
    99. y''-x*y'-x*y-x^n=0
    100. y''-a*x*y'-b*x*y-c*x^n=0
    101. y''-y'-x*y-x=0
    102. y''-y'-x*y-x^2=0
    103. y''-y'-x*y-x^2-1=0
    104. y''-2*y'-x*y-x^2-2=0
    105. y''-4*y'-x*y-x^2-4=0
    106. y''-y'-x*y-x^3-x^2+1=0
    107. y''-2y'-x*y-x^3-x^2=0
    108. y''-y'-x*y-x^3+2=0
    109. y''-2y'-x*y-x^3+2=0
    110. y''-4y'-x*y-x^3+2=0
    111. y''-6y'-x*y-x^3+2=0
    112. y''-8y'-x*y-x^3+2=0
    113. y''-y'-x*y-x^4+3=0
    114. .......
    115. y''-y'-x*y-x^n=0
    116. y''-a*y'-b*x*y-c*x^n=0
    117. y''-x*y-x^3+2=0
    118. y''-x*y-x^6+40=0
    119. .......
    120. y''-x*y-x^n=0
    121. y''-x*y-x^6-x^3+42=0
    122. y''-x^2*y-x^2=0
    123. y''-x^2*y-x^3=0
    124. y''-x^2*y-x^4=0
    125. y''-x^2*y-x^4+2=0
    126. y''-2x^2*y-x^4+1=0
    127. y''-x^3*y-x^3=0
    128. y''-x^3*y-x^4=0
    129. .......
    130. y''-x^n*y-x^n=0
    131. y''-x^2*y'-x*y-x^2=0
    132. y''-x^2*y'-x*y-2x^2=0
    133. y''-x^2*y'-x*y-3x^2=0
    134. .......
    135. y''-x^2*y'-x*y-n*x^2=0
    136. y''-x^3*y'-x^2*y-x^3=0
    137. y''-x^3*y'-x^3*y-x^3=0
    138. .......
    139. y''-x^n*y'-x^n*y-x^n=0
    140. y''-x^2*y'-x*y-x^2=0
    141. y''-x^2*y'-x^2*y-x^3-x^2=0
    142. y''-x^2*y'-x^3*y-x^4-x^2=0
    143. y''-x^3*y'-x*y-x^3-x^2=0
    144. y''-x^3*y'-x^2*y-x^3=0
    145. y''-x^3*y'-x^3*y-x^4-x^3=0
    146. y''-x^3*y'-x^2*y-2x^3=0
    147. y''-x^3*y'-x^2*y-3x^3=0
    148. y''-x^3*y'-x^2*y-4x^3=0
    149. .......
    150. y''-x^3*y'-x^2*y-n*x^3=0
    151. y''-1/x*y'-x*y-x^2-1/x=0
    152. y''-1/x*y'-x^2*y-x^3-1/x=0
    153. y''-1/x*y'-x^3*y-x^4-1/x=0

    154. y'' -y^2 =0
    155. y'' -y^3 =0
    156. y'' -y^2.5 =0
    157. y'' -y^3.5 =0

    158. y'*y'' -exp(y)=0
    159. y'*y'' -2exp(y)=0
    160. y'*y'' -3exp(y)=0

    161. y''-y^3-y=0
    162. y''-y^3+y=0
    163. y''+y^3-y=0
    164. y''+y^3+y=0

      Wolfram cannot solve

      Integral

    165. integrate f(x)
    166. integrate f(x)*x
    167. integrate(diff(F(x)),x,a,b)

    168. integrate x^x
    169. integrate(x^(-x))
    170. integrate(x^(2x))
    171. integrate(x^(n* x))

    172. integrate x^x/exp(x)
    173. integrate(x^(-x)/exp(x))
    174. integrate(x^(2x)/exp(x))
    175. integrate(x^(n* x)/exp(x))

      First order ode

    176. y'=sqrt(x)*cbrt(y)
    177. y'=sqrt(x)*cbrt(y-1)
    178. y'=sqrt(x)*cbrt(y-a)
    179. y'=sqrt(x-b)*cbrt(y)
    180. y'=sqrt(x-b)*cbrt(y-a)
    181. y'=1/sqrt(x)*cbrt(y)
    182. y'=1/sqrt(x)*cbrt(y-1)
    183. y'=1/qrt(x)*cbrt(y-a)
    184. y'=1/sqrt(x-b)*cbrt(y)
    185. y'=1/qrt(x-b)*cbrt(y-a)
    186. y'=cbrt(y)*x^n

    187. cbrt(y)* y'=sqrt(x)
    188. cbrt(y-1)*y'=sqrt(x)
    189. cbrt(y-a)* y'-sqrt(x)=0
    190. cbrt(y)* y'-sqrt(x-b)=0
    191. cbrt(y-a)* y'=sqrt(x-b)
    192. cbrt(y-x^2-1)+ y'=2x

      Second order ode

    193. y'' = sqrt(x+y+1)
    194. y'' = sqrt(x^2+y+1)-2
    195. y'' = 1/sqrt(x+y+1)
    196. y'' = 1/sqrt(x^2+y+1)-2
    197. y'' = cbrt(x+y+1)
    198. y'' = cbrt(x^2+y+1)-2
    199. y'' = 1/cbrt(x+y+1)
    200. y'' = 1/cbrt(x^2+y+1)-2
    201. y'' = (x+y+1)^1.5
    202. y'' = (x+y+1)^2.5
    203. y'' = (x+y+1)^3.5
    204. y'' = 1/(x+y+1)^1.5
    205. y'' = 1/(x+y+1)^2.5
    206. y'' = 1/(x+y+1)^3.5

    207. y'' -y^4 =0
    208. y'' -y^5 =0
    209. y'' -y^6 =0
    210. y'' -1/y^4 =0
    211. y'' -1/y^5 =0
    212. y'' -1/y^6 =0

    213. y''*y' -y^5 =0
    214. y''*y' -3y^6 =0
    215. y''*y' -4y^n =0

    216. y'' -x* y * y' =0
    217. y'' -x^2* y * y' =0
    218. y'' -x^3* y * y' =0
    219. y'' -x^n* y * y' =0

    220. y'' -y^3 *x =0
    221. y'' -y^4 *x =0
    222. y'' -y^5 *x =0
    223. y'' -y^n *x =0

    224. y'' -2y^4 *x =0
    225. y'' -2y^5 *x =0
    226. y'' -b*y^n *x =0

    227. y'' -sqrt(x) *y* y' =0
    228. y'' -2sqrt(x) *y* y' =0

    229. y'' -x^2 *y* y'=0
    230. y''- x^2*y *y' =0
    231. y''- x^3*y * y''' =0
    232. y''- x^4*y *y''' =0

    233. y'' +x*y*y' -x^2=0
    234. y'' -x*y*y' +x^2=0

    235. y'' - y^2 -x^2=0
    236. y''- 2y^2 -8x^2=0
    237. .......
    238. y'' +b*y^2 +c x^2=0

    239. y'' y' -exp(x)*y^2=0
    240. y''-exp(x)*y^2=0

    241. exp(x)*y''- y^2=0
    242. (x)*y''- y^2=0
    243. (x) *y'' - y^3=0
    244. (x^2)*y''- y^3=0
    245. (x^n)*y''- y^2=0
    246. exp(x)*y''- y*y'=0
    247. exp(x)*y''- y*y'=0
    248. y''-exp(x)*y*y'=0
    249. y''-exp(x)*y*y'=0
    250. y'' -exp(x)*y'=0
    251. y'*y'' -x*y =0
    252. y'*y'' -x^2*y^2 =0
    253. y'*y'' -x^m*y^n =0

    254. y^2*y'' -x =0
    255. y^2*y'' -a*x^2 =0
    256. y^2*y'' -x^2=0
    257. y^2*y'' -x^3=0
    258. y^2*y'' -x^n=0
    259. y^2*y'' -(1+x)^2=0
    260. y^2*y'' -(2+x)^3=0
    261. y^2*y'' -(3+x)^n=0
    262. exp(x)*y'' - y*y'=0
    263. 2exp(x)*y'' - y*y'=0

    264. y^3*y'' -x=0
    265. y^3*y'' -a*x^2 =0
    266. y^3*y'' -x^2=0
    267. y^3*y'' -x^3=0
    268. y^3*y'' -x^n=0

    269. y*y'*y'' =x
    270. y*y'*y'' =x^2
    271. y*y'*y'' =x^3
    272. y*y'*y'' =x^n

    273. y'' = exp(x)*y^2
    274. y'' = exp(x-1)*y^2
    275. y'' = exp(x-c)*y^2

    276. y'' = exp(x)*y^3
    277. y'' = exp(x-1)*y^3
    278. y'' = exp(x-c)*y^3

    279. y'' = exp(x)*y^n
    280. y'' = exp(x-1)*y^n
    281. y'' = exp(x-c)*y^n

    282. y'' = exp(y-x-c)
    283. y'' = exp(y)*x
    284. y'' = exp(y-x)*x
    285. y'' = exp(y-x-c)*x
    286. y'' = exp(y-x-1)*x^2
    287. y'' = exp(y-2x-c)*x^3
    288. y'' = exp(y-3x-c)*x^4
    289. y'' = exp(y-x-c)*x^5
    290. y'' = exp(y)*x^n
    291. y'' = exp(y-x)*x^n
    292. y'' = exp(y-x-c)*x^n

    293. y'' = exp(y-x^2-1)+2
    294. y'' = exp(y-x^2-x-2)+2
    295. y'' = exp(y-x^3-x-3)+6x
    296. y'' = exp(y-x^2-c)+2
    297. y'' = exp(y-x^2-x-c)+2
    298. y'' = exp(y-x^3-x-c)+6x

    299. y^2 *y''-x^2-4x-4=0
    300. 1/y^2 *y''-x^2-4x-4=0

    301. y*y'' -2x^2-x-1=0
    302. y*y'' -x^2=0
    303. y*y'' -x^3=0
    304. y*y'' -x^n=0
    305. y*y'' -(1+x)^2=0
    306. y*y'' -(2+x)^3=0
    307. y*y'' -(3+x)^n=0
    308. y*y'' -2x^2-b* x-c =0
    309. y* y''-x^3-3x^2-3x-1=0
    310. y* y''-3x^2-3x-1=0
    311. y* y''-3x-1=0
    312. y* y''-x^2-b*x-c =0
    313. y* y''-x^2-b*x =0
    314. y* y''-x^2-c =0
    315. y* y''-a*x^2-b*x-c =0
    316. y* y''-a*x^2-b*x =0
    317. y* y''-a*x^2-c =0
    318. y* y''-x-c =0
    319. y* y''-b*x-c =0

    320. y'' *(y-1)-x^2-4x-4 =0
    321. y'' *(y-1)-4x^2-4x-1 =0
    322. y'' *(y-1)-x^2- 4 =0
    323. y'' *(2y-1)-x^2-4x-4 =0
    324. y'' *(2y-1)-4x^2-4x-1 =0
    325. y'' *(2y-1)-x^2- 4 =0
    326. y'' *(2y-1)-4x-4 =0
    327. y'' *(2y-1)-x^2 =0
    328. y'' *(2y-1)-x =0
    329. y'' *(y-x-1)-x^2-4x-4 =0
    330. y'' *(y-x-1)-4x^2-4x-1 =0
    331. y'' *(y-x-1)-x^2- 4 =0
    332. y'' *(y-2x-1)-x^2-4x-4 =0
    333. y'' *(y-2x-1)-4x^2-4x-1 =0
    334. y'' *(y-2x-1)-x^2- 4 =0

    335. y*y'' -x -y'*x =0
    336. y*y'' -4x -y'*x =0
    337. y*y'' -x -2y'*x =0
    338. y*y'' -4x -2y'*x =0

      Third order ode

      It cannot seem to solve the high order nonlinear ODE.

    339. y''' -y^2 =0
    340. y''' -y^3 =0
    341. y''' -y^4 =0
    342. y''' -y^5 =0
    343. y''' -y^n =0

    344. y''' -sqrt(y) =0
    345. y''' -cbrt(y) =0
    346. y''' = exp(y)
    347. y''' -sqrt(x+y) =0
    348. y''' -cbrt(x+y) =0
    349. y''' = exp(x+y)
    350. y''' -sqrt(x^2+y) =0
    351. y''' -cbrt(x^2+y) =0
    352. y''' = exp(x^2+y)
    353. y''' -sqrt(x^2+x+y) =0
    354. y''' -cbrt(x^2+x+y) =0
    355. y''' = exp(x^2+x+y)
    356. y''' -sqrt(y+1) =0
    357. y''' -cbrt(y+1) =0
    358. y''' = exp(y+1)
    359. y''' -sqrt(x+y+1) =0
    360. y''' -cbrt(x+y+1) =0
    361. y''' = exp(x+y+1)
    362. y''' -sqrt(x^2+y+1) =0
    363. y''' -cbrt(x^2+y+1) =0
    364. y''' = exp(x^2+y+1)
    365. y''' -sqrt(x^2+x+y+1) =0
    366. y''' -cbrt(x^2+x+y+1) =0
    367. y''' = exp(x^2+x+y+1)

    368. y''' -2y^2 =0
    369. y''' -3y^3 =0
    370. y''' -4y^4 =0
    371. y''' -5y^5 =0
    372. y''' -a*y^n =0

    373. y''' -1/y =0
    374. y''' -1/y^2 =0
    375. y''' -1/y^3 =0
    376. y''' -1/y^4 =0
    377. y''' -1/y^5 =0
    378. y''' -1/sqrt(y) =0
    379. y''' -1/cbrt(y) =0
    380. y''' = 1/exp(y)

    381. y''' -2y^2 *x =0
    382. y''' -3y^3 *x =0
    383. y''' -4y^4 *x =0
    384. y''' -5y^5 *x =0
    385. y''' -y^n *x =0

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

    387. y''' -2y^2 *x^2 =0
    388. y''' -2y^3 *x^2 =0
    389. y''' -2y^4 *x^2 =0
    390. y''' -y^5 *x^2 =0
    391. y''' -b*y^n *x^2 =0

    392. y'''-y^2-x^2 =0
    393. y'''-y^2-4x^2 =0
    394. y'''-y^2-x^4 =0
    395. y'''-y^2-4x^4 =0
    396. y'''-x*y^2-x^3 =0
    397. y'''-x^2*y^2-x^4 =0
    398. y'''-x*y^2-x^2* y=0
    399. y'''-x^2*y^2-x^3* y =0

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

    401. x*y''' -y* y' =0
    402. x^2*y''' -y* y' =0

    403. y''' -x *y* y' =0
    404. y''' -2x *y* y' =0
    405. y'''' -x *y* y'' =0
    406. y''' -x *y* y' =0

    407. y''' -x^2 *y* y'' =0
    408. y''' -x^3 *y* y'' =0
    409. y''' -x^2 *y* y'' =0

    410. y''' -sqrt(x) *y* y' =0
    411. y''' -sqrt(x) *y* y' =0

    412. y''' -x^2*y * y''' =0
    413. ......
    414. y''' -x^a *y* y''=0

    415. y'''-x^2*y'-x*y-x^2=0
    416. y'''-x^2*y'-x*y-2x^2=0
    417. y'''-x^2*y'-x*y-3x^2=0
    418. .......
    419. y'''-x^2*y'-x*y-c*x^2=0

    420. y'''-x^3*y'-x^2*y-x^3=0
    421. y'''-x^3*y'-x^2*y-2*x^3=0
    422. y'''-x^3*y'-x^2*y-3*x^3=0
    423. .......
    424. y'''-x^3*y'-x^2*y-c*x^3=0

    425. y'''-x*y'-x*y-x =0
    426. y'''-x*y'-x*y-x^2=0
    427. y'''-x*y'-x*y-x^3=0
    428. ......
    429. y''' -x*y'-x*y-x^n=0

    430. y''' -exp(x)*y^2=0
    431. ......
    432. y''' -exp(x)*y^2=0

    433. exp(x)*y''- y * y''' =0
    434. exp(x) *y''' - y^2=0
    435. ......
    436. exp(x)* y''' - y^2=0

    437. (x) *y''' - y^2=0
    438. (x) * y''' - y^2=0
    439. (x) * y''' - y^3=0
    440. ......
    441. (x) * y''' - y^p=0

    442. (x^2) *y''' - y^3=0
    443. ......
    444. (x^2) * y''' - y^3=0

    445. (x^n) *y''' - y^p=0
    446. ......
    447. (x^n)* y''' - y^p=0

    448. y''' -exp(x)*y*y'=0
    449. ......
    450. y''' -exp(x)*y*y'=0

    451. y''' - y*y'=0
    452. ......
    453. exp(x) * y''' - y*y'=0

    454. y'''-exp(x) *y' =0
    455. y''' -exp(x)*y * y'' =0
    456. ......
    457. y''' -exp(x)*y * y' =0

    458. exp(x)*y''' - y * y'' =0
    459. ......
    460. exp(x) * y''' - y* y''=0

    461. 3exp(x)*y''- y * y''' =0
    462. 4exp(x)*y''' - y * y'' =0
    463. ......
    464. a*exp(x) * y''' - y * y'' =0

    465. y'*y''' -x^2 =0
    466. y'*y''' -x^3 =0
    467. y'*y''' -x^4 =0
    468. y'*y''' -x^m =0
    469. y'*y''' -x-c =0
    470. y'*y''' -x^2 -b*x=0
    471. y'*y''' -a*x^2 -b*x-c=0
    472. y'*y''' -x*y =0
    473. y'*y''' -x^2*y^2 =0
    474. y'*y''' -x^m*y^n =0

    475. y^2*y''' -x^2=0
    476. y^2*y''' -x^3=0
    477. y^2*y''' -x^n=0

    478. y^2*y''' -(1+x)^2=0
    479. y^2*y''' -(2+x)^3=0
    480. y^2*y''' -(3+x)^n=0

    481. y^3*y''' -x^2=0
    482. y^3*y''' -x^3=0
    483. y^3*y''' -x^n=0

    484. y^m*y'' -x^n =0
    485. y^m*y''' -x^n =0

    486. y*y'*y''' =x
    487. y*y'*y''' =x^2
    488. y*y'*y''' =x^3
    489. y*y'*y''' =x^n

    490. y*y''*y''' =x
    491. y*y''*y''' =x^2
    492. y*y''*y''' =x^3
    493. y*y''*y''' =x^n

    494. y'*y''*y''' =x
    495. y'*y''*y''' =x^2
    496. y'*y''*y''' =x^3
    497. y'*y''*y''' =x^n

    498. y''' = exp(x)*y^2
    499. y''' = exp(x-1)*y^2
    500. y''' = exp(x-2)*y^2
    501. y''' = exp(x-3)*y^2
    502. y''' = exp(x-c)*y^2

    503. y''' = exp(x)*y^3
    504. y''' = exp(x-1)*y^3
    505. y''' = exp(2x-2)*y^3
    506. y''' = exp(x-3)*y^3
    507. y''' = exp(2x-c)*y^3
    508. y''' = exp(x)*y^m
    509. y''' = exp(a*x-b)*y^m

    510. y''' = exp(y-3x^2-3x-1)
    511. y''' = sqrt(y-3x^2-3x-1)
    512. y''' = cbrt(y-3x^2-3x-1)
    513. y''' = sin(y-3x^2-3x-1)
    514. y''' = sinh(y-3x^2-3x-1)

    515. y''' = exp(y-x^3-3x^2-3x-1)+6
    516. y''' = sqrt(y-x^3-3x^2-3x-1)+6
    517. y''' = cbrt(y-x^3-3x^2-3x-1)+6
    518. y''' = sin(y-x^3-3x^2-3x-1)+6
    519. y''' = tan(y-x^3-3x^2-3x-1)+6
    520. y''' = sinh(y-x^3-3x^2-3x-1)+6
    521. y''' = tanh(y-x^3-3x^2-3x-1)+6

    522. y'*y''' = exp(x)
    523. y'*y''' = exp(x-1)
    524. y'*y''' = exp(x-2)
    525. y'*y''' = exp(x-3)
    526. y'*y''' = exp(x-c)

    527. y'*y''*y''' = exp(x)
    528. y'*y'' = exp(x)*y'''
    529. y''*y''' = exp(x)*y'
    530. y'*y''' = exp(x)*y''
    531. y''' = exp(x) *y' *y''
    532. y''' = exp(x) *y' *y
    533. y''' = exp(x) *y'' *y
    534. y''' = exp(x+y)
    535. y''' = exp(x)*y'
    536. y''' = exp(x)*y''

    537. y''' = exp(y)
    538. y''' = exp(y-1)
    539. y''' = 2exp(y)
    540. y''' = 3exp(y-1)
    541. y''' = y' exp(y)
    542. y''' = y'' exp(y)
    543. y''' y' = exp(y)
    544. y''' y''= exp(y)
    545. y''' = exp(y)
    546. y''' = a *exp(y+c)
    547. y''' = y' *exp(y+c)
    548. y'''* y'' = exp(y+c)

    549. y*y''' -x^2=0
    550. y*y''' -x^3=0
    551. y*y''' -x^n=0
    552. y*y''' -(1+x)^2=0
    553. y*y''' -(2+x)^3=0
    554. y*y''' -(3+x)^n=0
    555. y*y''' -3x^3-b*x^2-c*x-d =0
    556. y*y'''-6x^3-2x^2-2x-1 =0
    557. y*y'''-2x^3-2x^2-2x =0
    558. y*y'''-x^3-2x^2-2x-1 =0
    559. y*y'''-x^3-b*x^2-c*x-d =0
    560. y*y'''-x^3-b*x^2-c*x =0
    561. y*y'''-x^3-b*x^2 =0
    562. y*y'''-x^3-b*x^2-d =0
    563. y*y'''-x^3-c*x-d =0
    564. y*y'''-a*x^3-b*x^2-c*x-d =0
    565. y*y'''-a*x^3-b*x^2-c*x =0
    566. y*y'''-a*x^3-b*x^2 =0
    567. y*y'''-a*x^3-b*x^2-d =0
    568. y*y'''-a*x^3-c*x-d =0
    569. y*y'''- x^2 =0
    570. y*y'''- 2x^2 =0
    571. y*y'''- 3x^2 =0
    572. y*y'''- a*x^2 =0

    573. y* y'''-x^n =0
    574. y* y'''-2x^n =0
    575. y* y'''-3x^n =0
    576. y* y'''-a*x^n-b*x-c =0

    577. y*y'''-y^3-x^2 =0
    578. y*y'''-y^3-4x^2 =0
    579. y*y'''-y^3-x^4 =0
    580. y*y'''-y^3-4x^4 =0
    581. y*y'''-x*y^3-x^3 =0
    582. y*y'''-x^2*y^3-x^2 =0
    583. y*y'''-x*y^3-x^4=0
    584. y*y'''-x^2*y^3-x^6=0
    585. y*y'''-x*y^3-4x^3 =0
    586. y*y'''-x^2*y^3-4x^2 =0
    587. y*y'''-x*y^3-4x^4=0
    588. y*y'''-x^2*y^3-4x^6=0

    589. y*y''' -x -y' =0
    590. y*y''' -2x -y' =0
    591. y*y''' -x -2y' =0
    592. y*y''' -4x -2y' =0

    593. y*y''' -x -y''*x =0
    594. y*y''' -2x -y''*x =0
    595. y*y''' -x -2y''*x =0
    596. y*y''' -4x -2y''*x =0

    597. y'''+y* y''-3x^2-3x-1=0
    598. y'''+y* y''-3x^2-1=0
    599. y'''+y* y''-x^2-b*x-c =0
    600. y'''+y* y''-x^2-b*x =0
    601. y'''+y* y''-x^2-c =0
    602. y'''+y* y''-a*x^2-b*x-c =0
    603. y'''+y* y''-a*x^2-b*x =0
    604. 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.
    605. y*y'''' -x^2=0
    606. y*y'''' -x^3=0
    607. y*y'''' -x^n=0
    608. y*y'''' -(1+x)^2=0
    609. y*y'''' -(2+x)^3=0
    610. y*y'''' -(3+x)^n=0
    611. y*y'''' -a*x^4-b*x^3-c*x^2-d*x-f =0

    612. y'*y'''' -x^2 =0
    613. y'*y'''' -x^3 =0
    614. y'*y'''' -x^4 =0
    615. y'*y'''' -x^m =0
    616. y'*y'''' -x^2 -4x-4=0
    617. y'*y'''' -x^3 -b*x^2-c*x=0
    618. y'*y'''' -a*x^3 -b*x^2-c*x+f=0
    619. y'*y'''' -x*y =0
    620. y'*y'''' -x^2*y^2 =0
    621. y'*y'''' -x^m*y^n =0

    622. y''*y'''' -x^2 -b*x-c=0
    623. y''*y'''' -x^2-c*x=0
    624. y''*y'''' -x-c =0
    625. y''*y'''' -b*x^2-c*x+f=0
    626. y''*y'''' -x^2*y^2 =0
    627. y''*y'''' -x^m*y^n =0

      ... ...

      fractional order

    628. It cannot solve fractional calculus
    629. if the order of all these equations changed to fractional order, wolfram cannot solve too.
    630. fractional order differential equations,
    631. pi-order differential equations,
    632. negative order differential equations,
    633. complex order differential equations,
    634. variable order differential equations
    635. fractional order integral equations,
    636. double integral equations,
    637. Equation of mixed Fractional differential and integral orders
    638. fractional order partial differential equations,
    639. fractional order partial integral equations,
    640. complex order partial differential equations,
    mathHand.com can solve all above and below examples. wolfram also cannot solve or cannot find simple solution in below examples: 
    See Also