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Wolfram Bugs

There are bugs in many software such as WolframAlpha. Wish wolfram fix the bugs. the bugs are classified into few classes:

Wolfram solutions are wrong :

  1. y"-y'*y-x=0
  2. y"-y'*y-2x=0
  3. y''- y y'-3x=0
  4. ......
  5. y''- y y' -c x=0, where c= 1,2,3, ..... is any number.
    Wolfram solution always is 2/(c1-x) for above equations.

  6. y"+y'*y+x=0
  7. y"+y'*y+2x=0
  8. y''+ y y'+3x=0
  9. ......
  10. y''+ y y' +c x=0, where c= 1,2,3, ..... is any number.
    Wolfram solution always is 2/(c1+x) for above equations.

  11. y''-2 y y'-x=0
  12. y''-2 y y'-2x=0
  13. y''-2 y y'-3x=0
  14. ......
  15. y''-2 y y' -c x=0, where c= 1,2,3, ..... is any number.
    Wolfram solution always is 1/(c1-x) for above equations.

  16. y''-b y y'-x=0
  17. y''-b y y'-2x=0
  18. y''-b y y'-3x=0
  19. ......
  20. y''-b y y' -c x=0, where b=1,2,3, ....., c=1,2,3, ..... are any number.
    Wolfram solution always is 2/(b (c1-x)) for above equations.

  21. y'-y^2-2x^2-1=0
  22. y'-y^2-x^2-3=0
  23. y'-y^x-x^2-x-1=0
  24. y'-y^x-x^2-x=0
  25. ......
  26. y'- y^2 -b x^2 =0, where a,b,c,d= 1,2,3, ..... are any number.
  27. y'-y^2 -b x^2-c =0, where b,c,d= 1,2,3, ..... are any number.
  28. y'-y^2 -b x^2-c x =0, where b,c,d= 1,2,3, ..... are any number.
  29. y'-y^2 -b x^2-c x-d=0, where b,c,d= 1,2,3, ..... are any number.
    Wolfram solution always is 1/(c1-x) for above equations.

  30. y'-2y^2-2x^2-1=0
  31. y'-2y^2-x^2-3x=0
  32. y'-2y^2-x^2-x-1=0
  33. ......
  34. y'-2 y^2 -b x^2 =0, where a,b,c,d= 1,2,3, ..... are any number,
  35. y'-2y^2 -b x^2-c =0, where b,c= 1,2,3, ..... are any number,
  36. y'-2y^2 -b x^2-c x =0, where b,c= 1,2,3, ..... are any number,
    Wolfram solution always is 1/(2 (c1-x)) for above equations.

  37. y'-a y^2 -b x^2 =0, where a,b,c,d= 1,2,3, ..... are any number,
  38. y'-a y^2 -b x^2-c x =0, where a,b,c,d= 1,2,3, ..... are any number,
  39. y'-a y^2 -b x^2-d =0, where a,b,c,d= 1,2,3, ..... are any number,
  40. y'-a y^2 -b x^2-c x-d=0, where a,b,c,d= 1,2,3, ..... are any number,
    Wolfram solution always is 1/(a (c1-x)) for above equations.

  41. y'-a y^2 -y-b x^2 =0, where a,b,c,d= 1,2,3, ..... are any number,
  42. y'-a y^2 -y-b x^2-c x =0, where a,b,c,d= 1,2,3, ..... are any number,
  43. y'-a y^2 -y-b x^2-d =0, where a,b,c,d= 1,2,3, ..... are any number,
  44. y'-a y^2 -y-b x^2-c x-d=0, where a,b,c,d= 1,2,3, ..... are any number,
    Wolfram solution always is 1/(a (c1-x))-1/(2a) for above equations.

  45. y'-a y^2 -f y-b x^2 =0, where a,b,c,d= 1,2,3, ..... are any number,
  46. y'-a y^2 -f y-b x^2-c x =0, where a,b,c,d= 1,2,3, ..... are any number,
  47. y'-a y^2 -f y-b x^2-d =0, where a,b,c,d= 1,2,3, ..... are any number,
  48. y'-a y^2 -f y-b x^2-c x-d=0, where a,b,c,d= 1,2,3, ..... are any number,
    Wolfram solution always is 1/(a (c1-x))-f/(2a) for above equations.

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

  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, where c= 1,2,3, ..... is any number.
    Wolfram solution always is 2/(c1+x) for above equations.

  54. y' *(y^2+x)-2y =0

  55. y' y'' -x^2-1=0
  56. y' y'' -x^2-2=0
  57. y' y'' -x^2-3=0
  58. y' y'' -x^2+1=0
  59. y' y'' -x^2+2=0
  60. y' y'' -x^2+3=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

    Wolfram missing one solution in follwoing equations with two solutions :

  67. y"-y'*y=0
  68. y''-c y y'=0, where c=1,2,3, ... is any number,

  69. x*y" -y * y' =0
  70. 2x*y" -y * y' =0
  71. c*x*y''- y y'=0, where c=1,2,3, ... is any number,

    Wolfram cannot find SIMPLE solution :

  72. y' (y^2+x)-3y =0
  73. y' (y^2+x)-4y =0

  74. y" -y^2 =0
  75. y" -y^3 =0
  76. y" -y^2.5 =0
  77. y" -y^3.5 =0

  78. y" y'-y=0
  79. y" y'-2y=0
  80. y" y'-3y=0
  81. y" y'-c*y=0
  82. y"-x*y'-x*y-x=0
  83. y"-x*y'-x*y-2x=0
  84. y"-x*y'-x*y-3x=0
  85. .......
  86. y"-x*y'-x*y-n*x=0 where n=1,2,3 ......
  87. y"-x*y'-x*y-x^2-x=0
  88. y"-x*y'-x*y-x^3+2=0
  89. y"-x*y'-x*y-x^4-6=0
  90. y"-x*y'-x*y-x^5+24=0
  91. .......
  92. y"-x*y'-x*y-x^n=0, where n=1,2,3 ......
  93. y"-a*x*y'-b*x*y-c*x^n=0, where n=1,2,3 ......
  94. y"-y'-x*y-x=0
  95. y"-y'-x*y-x^2=0
  96. y"-y'-x*y-x^2-1=0
  97. y"-2*y'-x*y-x^2-2=0
  98. y"-4*y'-x*y-x^2-4=0
  99. y"-y'-x*y-x^3-x^2+1=0
  100. y"-2y'-x*y-x^3-x^2=0
  101. y"-y'-x*y-x^3+2=0
  102. y"-2y'-x*y-x^3+2=0
  103. y"-4y'-x*y-x^3+2=0
  104. y"-6y'-x*y-x^3+2=0
  105. y"-8y'-x*y-x^3+2=0
  106. y"-y'-x*y-x^4+3=0
  107. .......
  108. y"-y'-x*y-x^n=0, where n=1,2,3......
  109. y"-a*y'-b*x*y-c*x^n=0, where n=1,2,3 ......
  110. y"-x*y-x^3+2=0
  111. y"-x*y-x^6+40=0
  112. .......
  113. y"-x*y-x^n=0, where n=1,2,3 ......
  114. y"-x*y-x^6-x^3+42=0
  115. y"-x^2*y-x^2=0
  116. y"-x^2*y-x^3=0
  117. y"-x^2*y-x^4=0
  118. y"-x^2*y-x^4+2=0
  119. y"-2x^2*y-x^4+1=0
  120. y"-x^3*y-x^3=0
  121. y"-x^3*y-x^4=0
  122. .......
  123. y"-x^n*y-x^n=0, where n=1,2,3 ......
  124. y"-x^2*y'-x*y-x^2=0
  125. y''-x^2*y'-x*y-2x^2=0
  126. y''-x^2*y'-x*y-3x^2=0
  127. .......
  128. y''-x^2*y'-x*y-n*x^2=0, where n=1,2,3, ......
  129. y''-x^3*y'-x^2*y-x^3=0
  130. y"-x^3*y'-x^3*y-x^3=0
  131. .......
  132. y"-x^n*y'-x^n*y-x^n=0, where n=1,2,3, ......
  133. y"-x^2*y'-x*y-x^2=0
  134. y"-x^2*y'-x^2*y-x^3-x^2=0
  135. y"-x^2*y'-x^3*y-x^4-x^2=0
  136. y"-x^3*y'-x*y-x^3-x^2=0
  137. y"-x^3*y'-x^2*y-x^3=0
  138. y"-x^3*y'-x^3*y-x^4-x^3=0
  139. y''-x^3*y'-x^2*y-2x^3=0
  140. y''-x^3*y'-x^2*y-3x^3=0
  141. y''-x^3*y'-x^2*y-4x^3=0
  142. .......
  143. y''-x^3*y'-x^2*y-n*x^3=0, where n=1,2,3,......
  144. y"-1/x*y'-x*y-x^2-1/x=0
  145. y"-1/x*y'-x^2*y-x^3-1/x=0
  146. y"-1/x*y'-x^3*y-x^4-1/x=0

  147. y' y'' -exp(y)=0
  148. y' y'' -2exp(y)=0
  149. y' y'' -3exp(y)=0
  150. y''-y^3-y=0
  151. y''-y^3+y=0
  152. y''+y^3-y=0
  153. y''+y^3+y=0

    Wolfram cannot solve :

  154. integrate x^x
  155. integrate(x^(-x))
  156. integrate(x^(2x))
  157. integrate(x^(n* x))

  158. integrate x^x/exp(x)
  159. integrate(x^(-x)/exp(x))
  160. integrate(x^(2x)/exp(x))
  161. integrate(x^(n* x)/exp(x))

  162. y'''-y^2-x^2 =0
  163. y'''-y^2-4x^2 =0
  164. y'''-y^2-x^4 =0
  165. y'''-y^2-4x^4 =0
  166. y'''-x*y^2-x^3 =0
  167. y'''-x^2*y^2-x^4 =0
  168. y'''-x*y^2-x^2* y=0
  169. y'''-x^2*y^2-x^3* y =0

  170. y" -y^4 =0
  171. y" -y^5 =0
  172. y" -y^n =0 where n>3

  173. y" -2y^4 =0
  174. y" -3y^5 =0
  175. y" -4y^n =0 where n>3

  176. y" -1/y^3 =0
  177. y" -1/y^4 =0
  178. y" -1/y^5 =0
  179. y" -1/y^n =0 where n>3

  180. y"' -y^2 =0
  181. y'" -y^3 =0
  182. y"' -y^4 =0
  183. y'" -y^5 =0
  184. y"' -y^n =0 where n>1

  185. y"' -2y^2 =0
  186. y'" -2y^3 =0
  187. y"' -2y^4 =0
  188. y"' -3y^5 =0
  189. y"' -4y^n =0 where n>1

  190. y'" -1/y^3 =0
  191. y"' -1/y^4 =0
  192. y"' -1/y^5 =0
  193. y"' -1/y^n =0 where n>1

  194. y" -y^3 *x =0
  195. y" -y^4 *x =0
  196. y" -y^5 *x =0
  197. y" -y^n *x =0 where n>1

  198. y"' -2y^2 *x =0
  199. y"' -3y^3 *x =0
  200. y"' -4y^4 *x =0
  201. y"' -5y^5 *x =0
  202. y"' -y^n *x =0 where n>1

  203. d^n/dx^n y -y^m *x =0 where n<>m > 1

  204. y" -2y^4 *x =0
  205. y" -2y^5 *x =0
  206. y" -b*y^n *x =0 where b,n >1
  207. y"' -2y^2 *x =0
  208. y"' -2y^3 *x =0
  209. y"' -2y^4 *x =0
  210. y"' 2-y^5 *x =0
  211. y"' -b*y^n *x =0 where b,n>1

  212. d^n/dx^n y -b*y^m *x =0 where b, n<>m >1

  213. y" -x* y * y' =0
  214. y" -x^2* y * y' =0
  215. y" -x^3* y * y' =0
  216. y" -x^n* y * y' =0 where n>1

  217. x*y''' -y* y' =0
  218. x^2*y''' -y* y' =0

  219. y'' -2x *y* y' =0
  220. y''' -2x *y* y' =0
  221. y'''' -x *y* y'' =0
  222. d^n/dx^n y -x *y* y' =0 where n>1 is order number

  223. y''' -x^2 *y* y'' =0
  224. y''' -x^3 *y* y'' =0
  225. d^n/dx^n y -x^2 *y* y'' =0 where n>1 is order number

  226. y'' -sqrt(x) *y* y' =0
  227. y'' -2sqrt(x) *y* y' =0
  228. y''' -sqrt(x) *y* y' =0
  229. d^n/dx^n y -sqrt(x) *y* y' =0 where n>1 is order number

  230. y'' -x^2 *y* y'=0
  231. y''- x^2 y y' =0
  232. y''- x^3 y d^n/dx^n y =0 where n>1 is order number
  233. y''- x^4 y d^n/dx^n y =0 where n>1 is order number
  234. y''' -x^2 y d^n/dx^n y =0 where n is order number
  235. ......
  236. d^m/dx^m y -x^a y d^n/dx^n y =0 where n <> m >1 order number

  237. y" +x y y' -x^2=0
  238. y" -x y y' +x^2=0

  239. y" - y^2 -x^2=0
  240. y"- 2y^2 -8x^2=0
  241. .......
  242. y" +b y^2 +c x^2=0 where b=1,2,3, ...... and c=1,2,3, ...... are any numbers

  243. y'''-x^2*y'-x*y-x^2=0
  244. y'''-x^2*y'-x*y-2x^2=0
  245. y'''-x^2*y'-x*y-3x^2=0
  246. .......
  247. y'''-x^2*y'-x*y-c*x^2=0 where c=1,2,3,......

  248. y'''-x^3*y'-x^2*y-x^3=0
  249. y'''-x^3*y'-x^2*y-2*x^3=0
  250. y'''-x^3*y'-x^2*y-3*x^3=0
  251. .......
  252. y'''-x^3*y'-x^2*y-c*x^3=0 where c=1,2,3,......

  253. y'"-x*y'-x*y-x =0
  254. y'"-x*y'-x*y-x^2=0
  255. y'"-x*y'-x*y-x^3=0
  256. ......
  257. y''' -x*y'-x*y-x^n=0 where n>1 ......

  258. y'' y-exp(x) y^2=0
  259. y''-exp(x) y^2=0 second order
  260. y''' -exp(x) y^2=0
  261. ......
  262. d^n/dx^n y -exp(x) y^2=0 where n>1 order number

  263. exp(x) y' y - y^2=0
  264. exp(x) y''- y^2=0
  265. exp(x) y''' - y^2=0
  266. ......
  267. exp(x) d^n/dx^n y - y^2=0 where n>1 order number

  268. (x) y''- y^2=0
  269. (x) y''' - y^2=0
  270. (x) y'' - y^3=0
  271. (x) d^n/dx^n y - y^2=0 where n>1 order number
  272. (x) d^n/dx^n y - y^3=0 where n>1 order number
  273. ......
  274. (x) d^n/dx^n y - y^p=0 where n>1, p number

  275. (x^2) y''- y^3=0
  276. (x^2) y''' - y^3=0
  277. ......
  278. (x^2) d^n/dx^n y - y^3=0 where n>1 order number

  279. (x^n) y''- y^2=0
  280. (x^n) y''' - y^p=0
  281. ......
  282. (x^n) d^m/dx^m y - y^p=0 where m, n>1, p are number

  283. y''-exp(x) y y'=0
  284. y''-exp(x) y y'=0 second order
  285. y''' -exp(x) y y'=0
  286. ......
  287. d^n/dx^n y -exp(x) y y'=0 where n>1 order number

  288. exp(x) y''- y y'=0
  289. exp(x) y''- y y'=0
  290. y''' - y y'=0 Cannot find simple solution
  291. ......
  292. exp(x) d^n/dx^n y - y y'=0 where n>1 order number

  293. y'' -exp(x) y y'=0
  294. y''-exp(x) y d^n/dx^n y =0
  295. y''' -exp(x) y d^n/dx^n y =0
  296. ......
  297. d^m/dx^m y -exp(x) y d^n/dx^n y =0 where n <> m >1 order number

  298. exp(x) y'' - y y'=0
  299. exp(x) y''- y d^n/dx^n y =0
  300. exp(x) y''' - y d^n/dx^n y =0 where n <> m >1 order number
  301. ......
  302. exp(x) d^m/dx^m y - y `(d^n y)/dx^n`=0 where n <> m >1 order number

  303. 2exp(x) y'' - y y'=0
  304. 3exp(x) y''- y d^n/dx^n y =0
  305. 4exp(x) y''' - y d^n/dx^n y =0
  306. ......
  307. a*exp(x) d^m/dx^m y - y *d^n/dx^n y=0 where n <> m >1 order number

  308. y' y'' -x y =0
  309. y' y'' -x^2 y^2 =0
  310. y' y'' -x^m y^n =0

  311. y' y''' -x^2 =0
  312. y' y''' -x^3 =0
  313. y' y''' -x^4 =0
  314. y' y''' -x^m =0
  315. y' y''' -x-c =0
  316. y' y''' -x^2 -b*x=0
  317. y' y''' -a*x^2 -b*x-c=0
  318. y' y''' -x y =0
  319. y' y''' -x^2 y^2 =0
  320. y' y''' -x^m y^n =0

  321. y' y'''' -x^2 =0
  322. y' y'''' -x^3 =0
  323. y' y'''' -x^4 =0
  324. y' y'''' -x^m =0
  325. y' y'''' -x^2 -4x-4=0
  326. y' y'''' -x^3 -b*x^2-c*x=0
  327. y' y'''' -a*x^3 -b*x^2-c*x+f=0
  328. y' y'''' -x y =0
  329. y' y'''' -x^2 y^2 =0
  330. y' y'''' -x^m y^n =0

  331. y'' y'''' -x^2 -b*x-c=0
  332. y'' y'''' -x^2-c*x=0
  333. y'' y'''' -x-c =0
  334. y'' y'''' -b*x^2-c*x+f=0
  335. y'' y'''' -x^2 y^2 =0
  336. y'' y'''' -x^m y^n =0

  337. y^2 y'' -x =0
  338. y^2 y'' -a x^2 =0
  339. y^2 y'' -x^2=0
  340. y^2 y'' -x^3=0
  341. y^2 y'' -x^n=0
  342. y^2 y''' -x^2=0
  343. y^2 y''' -x^3=0
  344. y^2 y''' -x^n=0

  345. y^2 y'' -(1+x)^2=0
  346. y^2 y'' -(2+x)^3=0
  347. y^2 y'' -(3+x)^n=0
  348. y^2 y''' -(1+x)^2=0
  349. y^2 y''' -(2+x)^3=0
  350. y^2 y''' -(3+x)^n=0

  351. y^3 y'' -x=0
  352. y^3 y'' -a x^2 =0
  353. y^3 y'' -x^2=0
  354. y^3 y'' -x^3=0
  355. y^3 y'' -x^n=0
  356. y^3 y''' -x^2=0
  357. y^3 y''' -x^3=0
  358. y^3 y''' -x^n=0

  359. y^m y'' -x^n =0
  360. y^m y''' -x^n =0

  361. y y' y'' =x
  362. y y' y'' =x^2
  363. y y' y'' =x^3
  364. y y' y'' =x^n

  365. y y' y''' =x
  366. y y' y''' =x^2
  367. y y' y''' =x^3
  368. y y' y''' =x^n

  369. y y'' y''' =x
  370. y y'' y''' =x^2
  371. y y'' y''' =x^3
  372. y y'' y''' =x^n

  373. y' y'' y''' =x
  374. y' y'' y''' =x^2
  375. y' y'' y''' =x^3
  376. y' y'' y''' =x^n

  377. y'' = exp(x) y^3
  378. y'' = exp(x-1) y^3
  379. y'' = exp(x-2) y^3
  380. y'' = exp(x-3) y^3
  381. y'' = exp(x-c) y^3

  382. y''' = exp(x) y^2
  383. y''' = exp(x-1) y^2
  384. y''' = exp(x-2) y^2
  385. y''' = exp(x-3) y^2
  386. y''' = exp(x-c) y^2

  387. y''' = exp(x) y^3
  388. y''' = exp(x-1) y^3
  389. y''' = exp(2x-2) y^3
  390. y''' = exp(x-3) y^3
  391. y''' = exp(2x-c) y^3
  392. `y^((n)) = exp(x) y^m` where order >2
  393. `y^((n)) = exp(a*x-b) y^m` where order >2

  394. y' y''' = exp(x)
  395. y' y''' = exp(x-1)
  396. y' y''' = exp(x-2)
  397. y' y''' = exp(x-3)
  398. y' y''' = exp(x-c)
  399. y' y'' y''' = exp(x)
  400. y' y'' = exp(x) y'''
  401. y'' y''' = exp(x) y'
  402. y' y''' = exp(x) y''
  403. y''' = exp(x) y' y''
  404. y''' = exp(x) y' y
  405. y''' = exp(x) y'' y
  406. `y^((n)) = exp(x)` where order n > 2
  407. `y^((n)) = y^((m)) exp(x)` where order n > 2
  408. `y^((n)) y^((m)) = exp(x)` where order n > 2

  409. y''' = exp(y)
  410. y''' = exp(y-1)
  411. y''' = 2exp(y)
  412. y''' = 3exp(y-1)
  413. y''' = y' exp(y)
  414. y''' = y'' exp(y)
  415. y''' y' = exp(y)
  416. y''' y''= exp(y)
  417. `y^((n)) = exp(y)` where order n > 2
  418. `y^((n)) = a exp(y+c)` where order n > 2
  419. `y^((n)) = y^((m)) exp(y+c)` where order n > 2
  420. `y^((n)) y^((m)) = exp(y+c)` where order n > 2

  421. y^2 *y''-x^2-4x-4=0
  422. 1/y^2 *y''-x^2-4x-4=0

  423. y y'' -2x^2-x-1=0
  424. y y'' -x^2=0
  425. y y'' -x^3=0
  426. y y'' -x^n=0
  427. y y'' -(1+x)^2=0
  428. y y'' -(2+x)^3=0
  429. y y'' -(3+x)^n=0
  430. y y'' -2x^2-b* x-c =0
  431. y* y''-x^3-3x^2-3x-1=0
  432. y* y''-3x^2-3x-1=0
  433. y* y''-3x-1=0
  434. y* y''-x^2-b*x-c =0
  435. y* y''-x^2-b*x =0
  436. y* y''-x^2-c =0
  437. y* y''-a*x^2-b*x-c =0
  438. y* y''-a*x^2-b*x =0
  439. y* y''-a*x^2-c =0
  440. y* y''-x-c =0
  441. y* y''-b*x-c =0

  442. y y''' -x^2=0
  443. y y''' -x^3=0
  444. y y''' -x^n=0
  445. y y''' -(1+x)^2=0
  446. y y''' -(2+x)^3=0
  447. y y''' -(3+x)^n=0
  448. y y''' -3x^3-b*x^2-c*x-d =0
  449. y*y'''-6x^3-2x^2-2x-1 =0
  450. y*y'''-2x^3-2x^2-2x =0
  451. y*y'''-x^3-2x^2-2x-1 =0
  452. y*y'''-x^3-b*x^2-c*x-d =0
  453. y*y'''-x^3-b*x^2-c*x =0
  454. y*y'''-x^3-b*x^2 =0
  455. y*y'''-x^3-b*x^2-d =0
  456. y*y'''-x^3-c*x-d =0
  457. y*y'''-a*x^3-b*x^2-c*x-d =0
  458. y*y'''-a*x^3-b*x^2-c*x =0
  459. y*y'''-a*x^3-b*x^2 =0
  460. y*y'''-a*x^3-b*x^2-d =0
  461. y*y'''-a*x^3-c*x-d =0
  462. y*y'''- x^2 =0
  463. y*y'''- 2x^2 =0
  464. y*y'''- 3x^2 =0
  465. y*y'''- a*x^2 =0

  466. y y'''' -x^2=0
  467. y y'''' -x^3=0
  468. y y'''' -x^n=0
  469. y y'''' -(1+x)^2=0
  470. y y'''' -(2+x)^3=0
  471. y y'''' -(3+x)^n=0
  472. y y'''' -a*x^4-b*x^3-c*x^2-d*x-f =0

  473. `y*y^((n))-x^n =0`
  474. `y*y^((n))-2x^n =0`
  475. `y*y^((n))-3x^n =0`
  476. `y*y^((n))-a*x^n-b*x-c =0`

  477. y y'' -x -y' x =0
  478. y y'' -4x -y' x =0
  479. y y'' -x -2y' x =0
  480. y y'' -4x -2y' x =0

  481. y y'''-y^3-x^2 =0
  482. y y'''-y^3-4x^2 =0
  483. y y'''-y^3-x^4 =0
  484. y y'''-y^3-4x^4 =0
  485. y y'''-x*y^3-x^3 =0
  486. y y'''-x^2*y^3-x^2 =0
  487. y y'''-x*y^3-x^4=0
  488. y y'''-x^2*y^3-x^6=0
  489. y y'''-x*y^3-4x^3 =0
  490. y y'''-x^2*y^3-4x^2 =0
  491. y y'''-x*y^3-4x^4=0
  492. y y'''-x^2*y^3-4x^6=0

  493. y y''' -x -y' =0
  494. y y''' -2x -y' =0
  495. y y''' -x -2y' =0
  496. y y''' -4x -2y' =0

  497. y y''' -x -y'' x =0
  498. y y''' -2x -y'' x =0
  499. y y''' -x -2y'' x =0
  500. y y''' -4x -2y'' x =0

  501. y'''+y* y''-3x^2-3x-1=0
  502. y'''+y* y''-3x^2-1=0
  503. y'''+y* y''-x^2-b*x-c =0
  504. y'''+y* y''-x^2-b*x =0
  505. y'''+y* y''-x^2-c =0
  506. y'''+y* y''-a*x^2-b*x-c =0
  507. y'''+y* y''-a*x^2-b*x =0
  508. y'''+y* y''-a*x^2-c =0

  509. y'' (y-1)-x^2-4x-4 =0
  510. y'' (y-1)-x^2-4x =0
  511. y'' (y-1)-x^2- 4 =0
  512. y'' (2y-1)-x^2-4x-4 =0
  513. y'' (2y-1)-x^2-4x =0
  514. y'' (2y-1)-x^2- 4 =0
  515. y'' (2y-1)-4x-4 =0
  516. y'' (2y-1)-x^2 =0
  517. y'' (2y-1)-x =0

  518. if the order of all these equations changed to fractional order, wolfram cannot solve too.
  519. fractional order differential equations,
  520. pi-order differential equations,
  521. negative order differential equations,
  522. complex order differential equations,
  523. variable order differential equations
  524. fractional order integral equations,
  525. double integral equations,
  526. Equation of mixed Fractional differential and integral orders
  527. fractional order partial differential equations,
  528. fractional order partial integral equations,
  529. 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