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# Wolfram Bugs >800

### Content

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^2-x^2-x-1=0
4. y'-y^2-x^2-x-11=0
5. y'-y^2-x^2-x=0
......
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. y'-2y^2-x^2-x-11=0
......
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
17. y'-2y^2 -b* x^2-c* x-d =0
Wolfram solution always is 1/(2 (c1-x)) for above equations.

18. y'-3y^2-2x^2-1=0
19. y'-3y^2-x^2-3x=0
20. y'-3y^2-x^2-x-1=0
21. y'-3y^2-x^2-x-11=0
.....
22. y'-3y^2 -b* x^2 =0
23. y'-3y^2 -b* x^2-c =0
24. y'-3y^2 -b* x^2-c* x =0
25. y'-3y^2 -b* x^2-c* x-d =0
Wolfram solution always is 1/(3 (c1-x)) for above equations.

26. y'-a*y^2 -b* x^2 =0
27. y'-a*y^2 -b* x^2-c* x =0
28. y'-a*y^2 -b* x^2-d =0
29. y'-a*y^2 -b* x^2-c* x-d=0
Wolfram solution always is 1/(a (c1-x)) for above equations.

30. y'-a*y^2 -y-b* x^2 =0
31. y'-a*y^2 -y-b* x^2-c *x =0
32. y'-a*y^2 -y-b* x^2-d =0
33. 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.

34. y'-a*y^2 -f*y-b*x^2 =0
35. y'-a*y^2 -f*y-b*x^2-c*x =0
36. y'-a*y^2 -f*y-b*x^2-d =0
37. 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

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

42. y''+y'*y+x=0
43. y''+y'*y+2x=0
44. y''+ y *y'+3x=0
......
45. y''+ y *y' +c *x=0
Wolfram solution always is 2/(c1+x) for above equations.

46. y''-2 y*y'-x=0
47. y''-2 y*y'-2x=0
48. y''-2 y*y'-3x=0
......
49. y''-2 y*y' -c *x=0
Wolfram solution always is 1/(c1-x) for above equations.

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

54. y''+y'*y+x=0
55. y''+y'*y+2x=0
56. y''+ y*y'+3x=0
......
57. y''+ y*y' +c*x=0
Wolfram solution always is 2/(c1+x) for above equations.

58. y''* y'-y(x)^n=0
59. 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

60. if adding a term to above equations become the partial differential equations, thier solutions are wrong too.
61. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-x == 0
62. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-x-1 == 0
63. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2x == 0
64. D[y[x, t], t] +D[y[x, t], x] -y^2-x^2-2x-1 == 0
65. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-x == 0
66. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-x-1 == 0
67. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-2x == 0
68. D[y[x, t], t] +D[y[x, t], x] -y^2-2x^2-2x-1 == 0
......
Wolfram solutions always is 1/(c1(x-t)-x)

## Wolfram cannot find SIMPLE solution

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

### first order ODE

69. y'= cbrt(y)
70. y'= 2*cbrt(y)
71. y'= 3*cbrt(y)
72. y'= (x)*cbrt(y)
73. y'= (x)^2*cbrt(y)
74. y'= (x)^3*cbrt(y)
75. y'= 2*(x)*cbrt(y)
76. y'= 2*x^2*cbrt(y)
77. y'= 2*(x)^3*cbrt(y)
78. y'= (x-1)*cbrt(y)
79. y'= (x-1)^2*cbrt(y)
80. y'= (x-1)^3*cbrt(y)
81. y'= (x)*cbrt(y-1)
82. y'= (x)^2*cbrt(y-1)
83. y'= (x)^3*cbrt(y-1)
84. y'= 2*(x-1)*cbrt(y)
85. y'= 2*(x-1)^2*cbrt(y)
86. y'= 2*(x-1)^3*cbrt(y)
87. y'= 2*(x)*cbrt(y-1)
88. y'= 2*(x)^2*cbrt(y-1)
89. y'= 2*(x)^3*cbrt(y-1)

90. y' *(y^2+x)-2y =0
91. y' *(y^2+x)-3y =0
92. y' *(y^2+x)-4y =0
93. y' *(y^2+x)+3y =0
94. y' *(y^2+x)+4y =0

95. y'^2-x*y'-y=0
96. y'^2-x*y'-2y=0
97. y'^2-2x*y'-y=0
98. y'^2-2x*y'-2y=0

99. y'-x/(y-x-1)=0
100. y'-(x-1)/(y-x-1)=0
101. y'-x/(y-x-11)=0
102. y'-(x-11)/(y-x-11)=0
103. y'-x/(y-2x-1)=0
104. y'-(x-11)/(y-x-1)=0
105. y'-1/(y-x-1)-1=0
106. y'= -1/(y-x-1)-1

### second order ODE

107. y''+y' +x*y+x*x+1=0
108. y''+y' +2x*y+2x*x+1=0

109. y'' *y'-y=0
110. y'' *y'-2y=0
111. y'' *y'-3y=0
112. y'' *y'-c*y=0

113. y''-y/(x+1)-1=0
114. y''-y/(2x+1)-1=0
115. y''-2y/(2x+1)-1=0

116. x*y''-y-1-x=0
117. x*y''-y-1-2x=0
118. x*y''-y+1-2x=0

119. x*y''-y-x=0
120. x*y''-y-2x=0
121. x*y''-2y-2x=0

122. y" -(x+y)^2 =0
123. y" -(x+y)^3 =0
124. y" -(x+y-1)^2 =0
125. y" -(x+y-1)^3 =0
126. y" -(x+y+1)^2 =0
127. y" -(x+y+1)^3 =0

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

129. y' *y'' -x^2-1=0
130. y' *y'' -x^2-2=0
131. y' *y'' -x^2-3=0
132. y' *y'' -x^2+1=0
133. y' *y'' -x^2+2=0
134. y' *y'' -x^2+3=0
135. y' *y'' +x^2-1=0
136. y' *y'' +x^2-2=0
137. y' *y'' +x^2-3=0
138. y' *y'' +x^2+1=0
139. y' *y'' +x^2+2=0
140. y' *y'' +x^2+c=0

141. y''*y'-y^2=0
142. y''*y'-y^3=0
143. y''*y'-y^4=0

144. y''-x*y'-x*y-x=0
145. y''-x*y'-x*y-2x=0
146. y''-x*y'-x*y-3x=0
.......
147. y''-x*y'-x*y-n*x=0
148. y''-x*y'-x*y-x^2-x=0
149. y''-x*y'-x*y-x^3+2=0
150. y''-x*y'-x*y-x^4-6=0
151. y''-x*y'-x*y-x^5+24=0
.......
152. y''-x*y'-x*y-x^n=0
153. y''-a*x*y'-b*x*y-c*x^n=0
154. y''-y'-x*y-x=0
155. y''-y'-x*y-x^2=0
156. y''-y'-x*y-x^2-1=0
157. y''-2*y'-x*y-x^2-2=0
158. y''-4*y'-x*y-x^2-4=0
159. y''-y'-x*y-x^3-x^2+1=0
160. y''-2y'-x*y-x^3-x^2=0
161. y''-y'-x*y-x^3+2=0
162. y''-2y'-x*y-x^3+2=0
163. y''-4y'-x*y-x^3+2=0
164. y''-6y'-x*y-x^3+2=0
165. y''-8y'-x*y-x^3+2=0
166. y''-y'-x*y-x^4+3=0
.......
167. y''-y'-x*y-x^n=0
168. y''-a*y'-b*x*y-c*x^n=0
169. y''-x*y-x^3+2=0
170. y''-x*y-x^6+40=0
.......
171. y''-x*y-x^n=0
172. y''-x*y-x^6-x^3+42=0
173. y''-x^2*y-x^2=0
174. y''-x^2*y-x^3=0
175. y''-x^2*y-x^4=0
176. y''-x^2*y-x^4+2=0
177. y''-2x^2*y-x^4+1=0
178. y''-x^3*y-x^3=0
179. y''-x^3*y-x^4=0
.......
180. y''-x^n*y-x^n=0
181. y''-x^2*y'-x*y-x^2=0
182. y''-x^2*y'-x*y-2x^2=0
183. y''-x^2*y'-x*y-3x^2=0
.......
184. y''-x^2*y'-x*y-n*x^2=0
185. y''-x^3*y'-x^2*y-x^3=0
186. y''-x^3*y'-x^3*y-x^3=0
.......
187. y''-x^n*y'-x^n*y-x^n=0
188. y''-x^2*y'-x*y-x^2=0
189. y''-x^2*y'-x^2*y-x^3-x^2=0
190. y''-x^2*y'-x^3*y-x^4-x^2=0
191. y''-x^3*y'-x*y-x^3-x^2=0
192. y''-x^3*y'-x^2*y-x^3=0
193. y''-x^3*y'-x^3*y-x^4-x^3=0
194. y''-x^3*y'-x^2*y-2x^3=0
195. y''-x^3*y'-x^2*y-3x^3=0
196. y''-x^3*y'-x^2*y-4x^3=0
.......
197. y''-x^3*y'-x^2*y-n*x^3=0
198. y''-1/x*y'-x*y-x^2-1/x=0
199. y''-1/x*y'-x^2*y-x^3-1/x=0
200. y''-1/x*y'-x^3*y-x^4-1/x=0

201. y'*y'' -exp(y)=0
202. y'*y'' -2exp(y)=0
203. y'*y'' -3exp(y)=0

204. y'' -y^2 =0
205. y'' -y^3 =0
206. y'' -y^2.5 =0
207. y'' -y^3.5 =0

208. y''-y^2+y=0
209. y''-y^2-4y-1=0
210. y''-y^2-2y-1=0
211. y''+y^2+2y=0
212. y''+y^2+2=0

213. y''-y^3-y=0
214. y''-y^3+y=0
215. y''+y^3-y=0
216. y''+y^3+y=0

## Wolfram cannot solve

### Integral

217. integrate f(x)
218. integrate f(x)*x
219. integrate(diff(F(x)),x,a,b)

220. integrate x^x
221. integrate(x^(-x))
222. integrate(x^(2x))
223. integrate(x^(n* x))

224. integrate x^x/x
225. integrate x^x/x^2
226. integrate x^x/exp(x)
227. integrate(x^(-x)/exp(x))
228. integrate(x^(2x)/exp(x))
229. integrate(x^(n* x)/exp(x))

### First order ode

230. y'= (x-1)*cbrt(y-1)
231. y'= (x-1)^2*cbrt(y-1)
232. y'= (x-1)^3*cbrt(y-1)
233. y'= (2*x-1)*cbrt(y-1)
234. y'= 2*(x-1)^2*cbrt(y-1)
235. y'= 2*(x-1)^3*cbrt(y-1)
236. y'=sqrt(x)*cbrt(y)
237. y'=sqrt(x)*cbrt(y-1)
238. y'=sqrt(x)*cbrt(y-a)
239. y'=sqrt(x-1)*cbrt(y)
240. y'=sqrt(x-1)*cbrt(y-a)
241. y'=sqrt(x-b)*cbrt(y)
242. y'=sqrt(x-b)*cbrt(y-a)
243. y'=1/sqrt(x)*cbrt(y)
244. y'=1/sqrt(x)*cbrt(y-1)
245. y'=1/sqrt(x)*cbrt(y-a)
246. y'=1/sqrt(x-1)*cbrt(y)
247. y'=1/qrt(x-2)*cbrt(y-a)
248. y'=1/sqrt(x-b)*cbrt(y)
249. y'=1/qrt(x-b)*cbrt(y-a)
250. y'=cbrt(y)*x^n

251. cbrt(y)* y'=sqrt(x)
252. cbrt(y-1)*y'=sqrt(x)
253. cbrt(y)* y'=sqrt(x-1)
254. cbrt(y-1)*y'=sqrt(x-1)
255. cbrt(y-a)* y'=sqrt(x)
256. cbrt(y)* y'=sqrt(x-b)
257. cbrt(y-a)* y'=sqrt(x-b)

258. cbrt(y-x-1)+ y'=x <
259. cbrt(y-x^2-1)+ y'=x

260. y'^3+2x*y'-2y-2y^2=0
261. y'^3+2x*y'-2y-2y^2=1
262. y'^3+2x*y'-2y-2y^2=2
263. y'^3+2x*y'-2y-4y^2=0
264. y'^3+2x*y'-2y-4y^2=1
265. y'^3+2x*y'-2y-4y^2=2
266. y'^3+2x*y'-2y-2y^2.5=0
267. y'^3+2x*y'-2y-2y^2.5=1
268. y'^3+2x*y'-2y-2y^2.5=2
269. y'^3+2x*y'-2y-4y^2.5=0
270. y'^3+2x*y'-2y-4y^2.5=1
271. y'^3+2x*y'-2y-4y^2.5=2
......

### Second order ode

272. y'' = sqrt(x+y+1)
273. y'' = sqrt(2x+y+1)
274. y'' = 1/sqrt(x+y+1)
275. y'' = 1/sqrt(2x+y+1)
276. y'' = cbrt(x+y+1)
277. y'' = cbrt(2x+y+1)
278. y'' = 1/cbrt(x+y+1)
279. y'' = 1/cbrt(2x+y+1)
280. y'' = (x+y+1)^1.5
281. y'' = (x+y+1)^2.5
282. y'' = (x+y+1)^3.5
283. y'' = 1/(x+y+1)^1.5
284. y'' = 1/(x+y+1)^2.5
285. y'' = 1/(x+y+1)^3.5
286. y'' = 1/(x+y+1)^4

287. y'' = x*sqrt(x+y+1)
288. y'' = x*sqrt(2x+y+1)
289. y'' = x/sqrt(x+y+1)
290. y'' = x/sqrt(2x+y+1)
291. y'' = x*cbrt(x+y+1)
292. y'' = x*cbrt(2x+y+1)
293. y'' = x/cbrt(x+y+1)
294. y'' = x/cbrt(2x+y+1)
295. y'' = x*(x+y+1)^0.5
296. y'' = x*(x+y+1)^1.5
297. y'' = x*(x+y+1)^2.5
298. y'' = x*(x+y+1)^3.5
299. y'' = x*(x+y+1)^4
300. y'' = x*(x+y+1)^0.5
301. y'' = x/(x+y+1)^1.5
302. y'' = x/(x+y+1)^2.5
303. y'' = x/(x+y+1)^3.5
304. y'' = x/(x+y+1)^4
......

305. y'' = (x-1)*sqrt(x+y+1)
306. y'' = (x-1)*sqrt(2x+y+1)
307. y'' = (x-1)/sqrt(x+y+1)
308. y'' = (x-1)/sqrt(2x+y+1)
309. y'' = (x-1)*cbrt(x+y+1)
310. y'' = (x-1)*cbrt(2x+y+1)
311. y'' = (x-1)/cbrt(x+y+1)
312. y'' = (x-1)/cbrt(2x+y+1)
313. y'' = (x-1)*(x+y+1)^0.5
314. y'' = (x-1)*(x+y+1)^1.5
315. y'' = (x-1)*(x+y+1)^2.5
316. y'' = (x-1)*(x+y+1)^3.5
317. y'' = (x-1)/(x+y+1)^1.5
318. y'' = (x-1)/(x+y+1)^2.5
319. y'' = (x-1)/(x+y+1)^3.5
320. y'' = (x-1)/(x+y+1)^4

321. y'' = (x^2-1)*sqrt(x+y+1)
322. y'' = (x^2-1)*sqrt(2x+y+1)
323. y'' = (x^2-1)/sqrt(x+y+1)
324. y'' = (x^2-1)/sqrt(2x+y+1)
325. y'' = (x^2-1)*cbrt(x+y+1)
326. y'' = (x^2-1)*cbrt(2x+y+1)
327. y'' = (x^2-1)/cbrt(x+y+1)
328. y'' = (x^2-1)/cbrt(2x+y+1)
329. y'' = (x^2-1)*(x+y+1)^0.5
330. y'' = (x^2-1)*(x+y+1)^2
331. y'' = (x^2-1)*(x+y+1)^3
332. y'' = (x^2-1)*(x+y+1)^4
333. y'' = (x^2-1)/(x+y+1)^0.5
334. y'' = (x^2-1)/(x+y+1)^2
335. y'' = (x^2-1)/(x+y+1)^3
336. y'' = (x^2-1)/(x+y+1)^4

337. y'' = (x^2-4x+4)*sqrt(x+y+1)
338. y'' = (x^2-4x+4)*sqrt(2x+y+1)
339. y'' = (x^2-4x+4)/sqrt(x+y+1)
340. y'' = (x^2-4x+4)/sqrt(2x+y+1)
341. y'' = (x^2-4x+4)*cbrt(x+y+1)
342. y'' = (x^2-4x+4)*cbrt(2x+y+1)
343. y'' = (x^2-4x+4)/cbrt(x+y+1)
344. y'' = (x^2-4x+4)/cbrt(2x+y+1)
345. y'' = (x^2-4x+4)*(x+y+1)^0.5
346. y'' = (x^2-4x+4)*(x+y+1)^1.5
347. y'' = (x^2-4x+4)*(x+y+1)^2.5
348. y'' = (x^2-4x+4)*(x+y+1)^3.5
349. y'' = (x^2-4x+4)/(x+y+1)^1.5
350. y'' = (x^2-4x+4)/(x+y+1)^2.5
351. y'' = (x^2-4x+4)/(x+y+1)^3.5
352. y'' = (x^2-4x+4)/(x+y+1)^4

353. y'' -y^4 =0
354. y'' -y^5 =0
355. y'' -y^6 =0
356. y'' -1/y^4 =0
357. y'' -1/y^5 =0
358. y'' -1/y^6 =0

359. y''*y' -y^5 =0
360. y''*y' -3y^6 =0
361. y''*y' -4y^n =0

362. y'' -x* y * y' =0
363. y'' -x^2* y * y' =0
364. y'' -x^3* y * y' =0
365. y'' -x^n* y * y' =0

366. y'' -y^3 *x =0
367. y'' -y^4 *x =0
368. y'' -y^5 *x =0
369. y'' -y^n *x =0

370. y'' -2y^4 *x =0
371. y'' -2y^5 *x =0
372. y'' -b*y^n *x =0

373. y'' -sqrt(x) *y* y' =0
374. y'' -2sqrt(x) *y* y' =0

375. y'' -x^2 *y* y'=0
376. y''- x^2*y *y' =0
377. y''- x^3*y * y''' =0
378. y''- x^4*y *y''' =0

379. y'' +x*y*y' -x^2=0
380. y'' -x*y*y' +x^2=0

381. y'' - y^2 -x^2=0
382. y''- 2y^2 -8x^2=0
.......
383. y'' +b*y^2 +c x^2=0

384. y'' y' -exp(x)*y^2=0
385. y''-exp(x)*y^2=0

386. exp(x)*y''- y^2=0
387. (x)*y''- y^2=0
388. (x) *y'' - y^3=0
389. (x^2)*y''- y^3=0
390. (x^n)*y''- y^2=0
391. exp(x)*y''- y*y'=0
392. exp(x)*y''- y*y'=0
393. y''-exp(x)*y*y'=0
394. y''-exp(x)*y*y'=0
395. y'' -exp(x)*y'=0
396. y'*y'' -x*y =0
397. y'*y'' -x^2*y^2 =0
398. y'*y'' -x^m*y^n =0

399. y^2*y'' -x =0
400. y^2*y'' -a*x^2 =0
401. y^2*y'' -x^2=0
402. y^2*y'' -x^3=0
403. y^2*y'' -x^n=0
404. y^2*y'' -(1+x)^2=0
405. y^2*y'' -(2+x)^3=0
406. y^2*y'' -(3+x)^n=0
407. exp(x)*y'' - y*y'=0
408. 2exp(x)*y'' - y*y'=0

409. y^3*y'' -x=0
410. y^3*y'' -a*x^2 =0
411. y^3*y'' -x^2=0
412. y^3*y'' -x^3=0
413. y^3*y'' -x^n=0

414. y*y'*y'' =x
415. y*y'*y'' =x^2
416. y*y'*y'' =x^3
417. y*y'*y'' =x^n

418. y'' = exp(x)*y^2
419. y'' = exp(x-1)*y^2
420. y'' = exp(x-c)*y^2

421. y'' = exp(x)*y^3
422. y'' = exp(x-1)*y^3
423. y'' = exp(x-c)*y^3

424. y'' = exp(x)*y^n
425. y'' = exp(x-1)*y^n
426. y'' = exp(x-c)*y^n

427. y'' = exp(y-x-c)
428. y'' = exp(y)*x
429. y'' = exp(y-x)*x
430. y'' = exp(y-x-c)*x
431. y'' = exp(y-x-1)*x^2
432. y'' = exp(y-2x-c)*x^3
433. y'' = exp(y-3x-c)*x^4
434. y'' = exp(y-x-c)*x^5
435. y'' = exp(y)*x^n
436. y'' = exp(y-x)*x^n
437. y'' = exp(y-x-c)*x^n

438. y'' = exp(y-x^2-1)+2
439. y'' = exp(y-x^2-x-2)+2
440. y'' = exp(y-x^3-x-3)+6x
441. y'' = exp(y-x^2-c)+2
442. y'' = exp(y-x^2-x-c)+2
443. y'' = exp(y-x^3-x-c)+6x

444. y^2 *y''-x^2-4x-4=0
445. y^2 *y''-x^2-4x=0
446. y^2 *y''-x^2-4=0

447. 1/y^2 *y''-x^2-4x-4=0
448. 1/y^2 *y''-x^2-4x=0
449. 1/y^2 *y''-x^2-4=0

450. y^4 *y''-x^2-4x-4=0
451. y^4 *y''-x^2-4x=0
452. y^4 *y''-x^2-4=0

453. 1/y^4 *y''-x^2-4x-4=0
454. 1/y^4 *y''-x^2-4x=0
455. 1/y^4 *y''-x^2-4=0

456. y^(1/2) *y''-x^2-4x-4=0
457. y^(1/2) *y''-x^2-4x=0
458. y^(1/2) *y''-x^2-4=0

459. 1/y^(1/2) *y''-x^2-4x-4=0
460. 1/y^(1/2) *y''-x^2-4x=0
461. 1/y^(1/2) *y''-x^2-4=0

462. y*y'' -2x^2-x-1=0
463. y*y'' -x^2=0
464. y*y'' -x^3=0
465. y*y'' -x^n=0
466. y*y'' -(1+x)*(x-2)=0
467. y*y'' -(1+x)*(2x+1)=0
468. y*y'' -(1+x)^2=0
469. y*y'' -(2+x)^3=0
470. y*y'' -(3+x)^n=0
471. y*y'' -2x^2-b* x-c =0
472. y* y''-x^3-3x^2-3x-1=0
473. y* y''-3x^2-3x-1=0
474. y* y''-3x-1=0
475. y* y''-x^2-b*x-c =0
476. y* y''-x^2-b*x =0
477. y* y''-x^2-c =0
478. y* y''-a*x^2-b*x-c =0
479. y* y''-a*x^2-b*x =0
480. y* y''-a*x^2-c =0
481. y* y''-x-c =0
482. y* y''-b*x-c =0

483. y'' *(y-1)-x^2-4x-4 =0
484. y'' *(y-1)-4x^2-4x-1 =0
485. y'' *(y-1)-x^2- 4 =0
486. y'' *(2y-1)-x^2-4x-4 =0
487. y'' *(2y-1)-4x^2-4x-1 =0
488. y'' *(2y-1)-x^2- 4 =0
489. y'' *(2y-1)-4x-4 =0
490. y'' *(2y-1)-x^2 =0
491. y'' *(2y-1)-x =0
492. y'' *(y-x-1)-x^2-4x-4 =0
493. y'' *(y-x-1)-4x^2-4x-1 =0
494. y'' *(y-x-1)-x^2- 4 =0
495. y'' *(y-2x-1)-x^2-4x-4 =0
496. y'' *(y-2x-1)-4x^2-4x-1 =0
497. y'' *(y-2x-1)-x^2- 4 =0

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

502. y''^2+x^2*y''-2y=0
503. y''^2+x^2*y''-2y=1
504. y''^2+x^2*y''-2y=2
505. y''^2+2x^2*y''-4y=0
506. y''^2+2x^2*y''-4y=1
507. y''^2+2x^2*y''-4y=2

### Third order ode

It cannot seem to solve the high order nonlinear ODE.

508. y''' -y^2 =0
509. y''' -y^3 =0
510. y''' -y^4 =0
511. y''' -y^5 =0
512. y''' -y^n =0

513. y''' -sqrt(y) =0
514. y''' -cbrt(y) =0
515. y''' = exp(y)
516. y''' -sqrt(x+y) =0
517. y''' -cbrt(x+y) =0
518. y''' = exp(x+y)
519. y''' -sqrt(x^2+y) =0
520. y''' -cbrt(x^2+y) =0
521. y''' = exp(x^2+y)
522. y''' -sqrt(x^2+x+y) =0
523. y''' -cbrt(x^2+x+y) =0
524. y''' = exp(x^2+x+y)
525. y''' -sqrt(y+1) =0
526. y''' -cbrt(y+1) =0
527. y''' = exp(y+1)
528. y''' -sqrt(x+y+1) =0
529. y''' -cbrt(x+y+1) =0
530. y''' = exp(x+y+1)
531. y''' -sqrt(x^2+y+1) =0
532. y''' -cbrt(x^2+y+1) =0
533. y''' = exp(x^2+y+1)
534. y''' -sqrt(x^2+x+y+1) =0
535. y''' -cbrt(x^2+x+y+1) =0
536. y''' = exp(x^2+x+y+1)

537. y''' -2y^2 =0
538. y''' -3y^3 =0
539. y''' -4y^4 =0
540. y''' -5y^5 =0
541. y''' -a*y^n =0

542. y''' -1/y =0
543. y''' -1/y^2 =0
544. y''' -1/y^3 =0
545. y''' -1/y^4 =0
546. y''' -1/y^5 =0
547. y''' -1/sqrt(y) =0
548. y''' -1/cbrt(y) =0
549. y''' = 1/exp(y)

550. y''' -2y^2 *x =0
551. y''' -3y^3 *x =0
552. y''' -4y^4 *x =0
553. y''' -5y^5 *x =0
554. y''' -y^n *x =0

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

556. y''' -2y^2 *x^2 =0
557. y''' -2y^3 *x^2 =0
558. y''' -2y^4 *x^2 =0
559. y''' -y^5 *x^2 =0
560. y''' -b*y^n *x^2 =0

561. y'''-y^2-x^2 =0
562. y'''-y^2-4x^2 =0
563. y'''-y^2-x^4 =0
564. y'''-y^2-4x^4 =0
565. y'''-x*y^2-x^3 =0
566. y'''-x^2*y^2-x^4 =0
567. y'''-x*y^2-x^2* y=0
568. y'''-x^2*y^2-x^3* y =0

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

570. x*y''' -y* y' =0
571. x^2*y''' -y* y' =0

572. y''' -x *y* y' =0
573. y''' -2x *y* y' =0
574. y'''' -x *y* y'' =0
575. y''' -x *y* y' =0

576. y''' -x^2 *y* y'' =0
577. y''' -x^3 *y* y'' =0
578. y''' -x^2 *y* y'' =0

579. y''' -sqrt(x) *y* y' =0
580. y''' -sqrt(x) *y* y' =0

581. y''' -x^2*y * y''' =0
582. ......
583. y''' -x^a *y* y''=0

584. y'''-x^2*y'-x*y-x^2=0
585. y'''-x^2*y'-x*y-2x^2=0
586. y'''-x^2*y'-x*y-3x^2=0
.......
587. y'''-x^2*y'-x*y-c*x^2=0

588. y'''-x^3*y'-x^2*y-x^3=0
589. y'''-x^3*y'-x^2*y-2*x^3=0
590. y'''-x^3*y'-x^2*y-3*x^3=0
.......
591. y'''-x^3*y'-x^2*y-c*x^3=0

592. y'''-x*y'-x*y-x =0
593. y'''-x*y'-x*y-x^2=0
594. y'''-x*y'-x*y-x^3=0
595. ......
596. y''' -x*y'-x*y-x^n=0

597. y''' -exp(x)*y^2=0
598. ......
599. y''' -exp(x)*y^2=0

600. exp(x)*y''- y * y''' =0
601. exp(x) *y''' - y^2=0
602. ......
603. exp(x)* y''' - y^2=0

604. (x) *y''' - y^2=0
605. (x) * y''' - y^2=0
606. (x) * y''' - y^3=0
607. ......
608. (x) * y''' - y^p=0

609. (x^2) *y''' - y^3=0
610. ......
611. (x^2) * y''' - y^3=0

612. (x^n) *y''' - y^p=0
613. ......
614. (x^n)* y''' - y^p=0

615. y''' -exp(x)*y*y'=0
616. ......
617. y''' -exp(x)*y*y'=0

618. y''' - y*y'=0
619. ......
620. exp(x) * y''' - y*y'=0

621. y'''-exp(x) *y' =0
622. y''' -exp(x)*y * y'' =0
623. ......
624. y''' -exp(x)*y * y' =0

625. exp(x)*y''' - y * y'' =0
626. ......
627. exp(x) * y''' - y* y''=0

628. 3exp(x)*y''- y * y''' =0
629. 4exp(x)*y''' - y * y'' =0
630. ......
631. a*exp(x) * y''' - y * y'' =0

632. y'*y''' -x^2 =0
633. y'*y''' -x^3 =0
634. y'*y''' -x^4 =0
635. y'*y''' -x^m =0
636. y'*y''' -x-c =0
637. y'*y''' -x^2 -b*x=0
638. y'*y''' -a*x^2 -b*x-c=0
639. y'*y''' -x*y =0
640. y'*y''' -x^2*y^2 =0
641. y'*y''' -x^m*y^n =0

642. y^2*y''' -x^2=0
643. y^2*y''' -x^3=0
644. y^2*y''' -x^n=0

645. y^2*y''' -(1+x)^2=0
646. y^2*y''' -(2+x)^3=0
647. y^2*y''' -(3+x)^n=0

648. y^3*y''' -x^2=0
649. y^3*y''' -x^3=0
650. y^3*y''' -x^n=0

651. y^m*y'' -x^n =0
652. y^m*y''' -x^n =0

653. y*y'*y''' =x
654. y*y'*y''' =x^2
655. y*y'*y''' =x^3
656. y*y'*y''' =x^n

657. y*y''*y''' =x
658. y*y''*y''' =x^2
659. y*y''*y''' =x^3
660. y*y''*y''' =x^n

661. y'*y''*y''' =x
662. y'*y''*y''' =x^2
663. y'*y''*y''' =x^3
664. y'*y''*y''' =x^n

665. y''' = exp(x)*y^2
666. y''' = exp(x-1)*y^2
667. y''' = exp(x-2)*y^2
668. y''' = exp(x-3)*y^2
669. y''' = exp(x-c)*y^2

670. y''' = exp(x)*y^3
671. y''' = exp(x-1)*y^3
672. y''' = exp(2x-2)*y^3
673. y''' = exp(x-3)*y^3
674. y''' = exp(2x-c)*y^3
675. y''' = exp(x)*y^m
676. y''' = exp(a*x-b)*y^m

677. y''' = exp(y-3x^2-3x-1)
678. y''' = sqrt(y-3x^2-3x-1)
679. y''' = cbrt(y-3x^2-3x-1)
680. y''' = sin(y-3x^2-3x-1)
681. y''' = sinh(y-3x^2-3x-1)

682. y''' = exp(y-x^3-3x^2-3x-1)+6
683. y''' = sqrt(y-x^3-3x^2-3x-1)+6
684. y''' = cbrt(y-x^3-3x^2-3x-1)+6
685. y''' = sin(y-x^3-3x^2-3x-1)+6
686. y''' = tan(y-x^3-3x^2-3x-1)+6
687. y''' = sinh(y-x^3-3x^2-3x-1)+6
688. y''' = tanh(y-x^3-3x^2-3x-1)+6

689. y'*y''' = exp(x)
690. y'*y''' = exp(x-1)
691. y'*y''' = exp(x-2)
692. y'*y''' = exp(x-3)
693. y'*y''' = exp(x-c)

694. y'*y''*y''' = exp(x)
695. y'*y'' = exp(x)*y'''
696. y''*y''' = exp(x)*y'
697. y'*y''' = exp(x)*y''
698. y''' = exp(x) *y' *y''
699. y''' = exp(x) *y' *y
700. y''' = exp(x) *y'' *y
701. y''' = exp(x+y)
702. y''' = exp(x)*y'
703. y''' = exp(x)*y''

704. y''' = exp(y)
705. y''' = exp(y-1)
706. y''' = 2exp(y)
707. y''' = 3exp(y-1)
708. y''' = y' exp(y)
709. y''' = y'' exp(y)
710. y''' y' = exp(y)
711. y''' y''= exp(y)
712. y''' = exp(y)
713. y''' = a *exp(y+c)
714. y''' = y' *exp(y+c)
715. y'''* y'' = exp(y+c)

716. y*y''' -x^2=0
717. y*y''' -x^3=0
718. y*y''' -x^n=0
719. y*y''' -(1+x)*(x+2)*(x+3)=0
720. y*y''' -(1+x)*(2x+1)*(3x+1)=0
721. y*y''' -(1+x)^2=0
722. y*y''' -(2+x)^3=0
723. y*y''' -(3+x)^n=0
724. y*y''' -3x^3-b*x^2-c*x-d =0
725. y*y'''-6x^3-2x^2-2x-1 =0
726. y*y'''-2x^3-2x^2-2x =0
727. y*y'''-x^3-2x^2-2x-1 =0
728. y*y'''-x^3-b*x^2-c*x-d =0
729. y*y'''-x^3-b*x^2-c*x =0
730. y*y'''-x^3-b*x^2 =0
731. y*y'''-x^3-b*x^2-d =0
732. y*y'''-x^3-c*x-d =0
733. y*y'''-a*x^3-b*x^2-c*x-d =0
734. y*y'''-a*x^3-b*x^2-c*x =0
735. y*y'''-a*x^3-b*x^2 =0
736. y*y'''-a*x^3-b*x^2-d =0
737. y*y'''-a*x^3-c*x-d =0
738. y*y'''- x^2 =0
739. y*y'''- 2x^2 =0
740. y*y'''- 3x^2 =0
741. y*y'''- a*x^2 =0

742. y* y'''-x^n =0
743. y* y'''-2x^n =0
744. y* y'''-3x^n =0
745. y* y'''-a*x^n-b*x-c =0

746. y*y'''-y^3-x^2 =0
747. y*y'''-y^3-4x^2 =0
748. y*y'''-y^3-x^4 =0
749. y*y'''-y^3-4x^4 =0
750. y*y'''-x*y^3-x^3 =0
751. y*y'''-x^2*y^3-x^2 =0
752. y*y'''-x*y^3-x^4=0
753. y*y'''-x^2*y^3-x^6=0
754. y*y'''-x*y^3-4x^3 =0
755. y*y'''-x^2*y^3-4x^2 =0
756. y*y'''-x*y^3-4x^4=0
757. y*y'''-x^2*y^3-4x^6=0

758. y*y''' -x -y' =0
759. y*y''' -2x -y' =0
760. y*y''' -x -2y' =0
761. y*y''' -4x -2y' =0

762. y*y''' -x -y''*x =0
763. y*y''' -2x -y''*x =0
764. y*y''' -x -2y''*x =0
765. y*y''' -4x -2y''*x =0

766. y'''+y* y''-3x^2-3x-1=0
767. y'''+y* y''-3x^2-1=0
768. y'''+y* y''-x^2-b*x-c =0
769. y'''+y* y''-x^2-b*x =0
770. y'''+y* y''-x^2-c =0
771. y'''+y* y''-a*x^2-b*x-c =0
772. y'''+y* y''-a*x^2-b*x =0
773. 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.
774. y*y'''' -x^2=0
775. y*y'''' -x^3=0
776. y*y'''' -x^n=0
777. y*y'''' -(1+x)*(x+2)*(x+3)*(x+4)=0
778. y*y'''' -(1+x)*(2x+1)*(x+2)*(x+3)=0
779. y*y'''' -(1+x)^2=0
780. y*y'''' -(2+x)^3=0
781. y*y'''' -(3+x)^n=0
782. y*y'''' -a*x^4-b*x^3-c*x^2-d*x-f =0

783. y'*y'''' -x^2 =0
784. y'*y'''' -x^3 =0
785. y'*y'''' -x^4 =0
786. y'*y'''' -x^m =0
787. y'*y'''' -x^2 -4x-4=0
788. y'*y'''' -x^3 -b*x^2-c*x=0
789. y'*y'''' -a*x^3 -b*x^2-c*x+f=0
790. y'*y'''' -x*y =0
791. y'*y'''' -x^2*y^2 =0
792. y'*y'''' -x^m*y^n =0

793. y''*y'''' -x^2 -b*x-c=0
794. y''*y'''' -x^2-c*x=0
795. y''*y'''' -x-c =0
796. y''*y'''' -b*x^2-c*x+f=0
797. y''*y'''' -x^2*y^2 =0
798. y''*y'''' -x^m*y^n =0

... ...

### fractional order

799. if the order of all these equations changed to fractional order, wolfram cannot solve too.
800. It cannot solve fractional calculus
801. fractional order differential equations,
802. pi-order differential equations,
803. negative order differential equations,
804. complex order differential equations,
805. variable order differential equations
806. fractional order integral equations,
807. double integral equations,
808. fractional order partial integral equations,
809. complex order partial differential equations,
810. Equation of mixed Fractional differential and integral orders
811. Equation of mixed Fractional partial differential and integral orders

### partial differential equation

812. if adding a term to above equations become the partial differential equations, wolfram has the same problem.
813. high order partial differential equations
814. 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 100 examples as follows: ﻿