﻿﻿﻿ math handbook calculator - Fractional Calculus Computer Algebra System software
+ + =

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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: ﻿