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Wolfram Bugs >800

Content

  1. Wolfram solutions are wrong
  2. Wolfram cannot find SIMPLE solution
  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 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/exp(x)
  225. integrate(x^(-x)/exp(x))
  226. integrate(x^(2x)/exp(x))
  227. integrate(x^(n* x)/exp(x))

    First order ode

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

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

  256. cbrt(y-x-1)+ y'=x <
  257. cbrt(y-x^2-1)+ y'=x

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

    Second order ode

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

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

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

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

  335. y'' = (x^2-4x+4)*sqrt(x+y+1)
  336. y'' = (x^2-4x+4)*sqrt(2x+y+1)
  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)*cbrt(x+y+1)
  340. y'' = (x^2-4x+4)*cbrt(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)*(x+y+1)^0.5
  344. y'' = (x^2-4x+4)*(x+y+1)^1.5
  345. y'' = (x^2-4x+4)*(x+y+1)^2.5
  346. y'' = (x^2-4x+4)*(x+y+1)^3.5
  347. y'' = (x^2-4x+4)/(x+y+1)^1.5
  348. y'' = (x^2-4x+4)/(x+y+1)^2.5
  349. y'' = (x^2-4x+4)/(x+y+1)^3.5
  350. y'' = (x^2-4x+4)/(x+y+1)^4

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

  357. y''*y' -y^5 =0
  358. y''*y' -3y^6 =0
  359. y''*y' -4y^n =0

  360. y'' -x* y * y' =0
  361. y'' -x^2* y * y' =0
  362. y'' -x^3* y * y' =0
  363. y'' -x^n* y * y' =0

  364. y'' -y^3 *x =0
  365. y'' -y^4 *x =0
  366. y'' -y^5 *x =0
  367. y'' -y^n *x =0

  368. y'' -2y^4 *x =0
  369. y'' -2y^5 *x =0
  370. y'' -b*y^n *x =0

  371. y'' -sqrt(x) *y* y' =0
  372. y'' -2sqrt(x) *y* y' =0

  373. y'' -x^2 *y* y'=0
  374. y''- x^2*y *y' =0
  375. y''- x^3*y * y''' =0
  376. y''- x^4*y *y''' =0

  377. y'' +x*y*y' -x^2=0
  378. y'' -x*y*y' +x^2=0

  379. y'' - y^2 -x^2=0
  380. y''- 2y^2 -8x^2=0
    .......
  381. y'' +b*y^2 +c x^2=0

  382. y'' y' -exp(x)*y^2=0
  383. y''-exp(x)*y^2=0

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

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

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

  412. y*y'*y'' =x
  413. y*y'*y'' =x^2
  414. y*y'*y'' =x^3
  415. y*y'*y'' =x^n

  416. y'' = exp(x)*y^2
  417. y'' = exp(x-1)*y^2
  418. y'' = exp(x-c)*y^2

  419. y'' = exp(x)*y^3
  420. y'' = exp(x-1)*y^3
  421. y'' = exp(x-c)*y^3

  422. y'' = exp(x)*y^n
  423. y'' = exp(x-1)*y^n
  424. y'' = exp(x-c)*y^n

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

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

  442. y^2 *y''-x^2-4x-4=0
  443. y^2 *y''-x^2-4x=0
  444. y^2 *y''-x^2-4=0

  445. 1/y^2 *y''-x^2-4x-4=0
  446. 1/y^2 *y''-x^2-4x=0
  447. 1/y^2 *y''-x^2-4=0

  448. y^4 *y''-x^2-4x-4=0
  449. y^4 *y''-x^2-4x=0
  450. y^4 *y''-x^2-4=0

  451. 1/y^4 *y''-x^2-4x-4=0
  452. 1/y^4 *y''-x^2-4x=0
  453. 1/y^4 *y''-x^2-4=0

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

  457. 1/y^(1/2) *y''-x^2-4x-4=0
  458. 1/y^(1/2) *y''-x^2-4x=0
  459. 1/y^(1/2) *y''-x^2-4=0

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

  479. y'' *(y-1)-x^2-4x-4 =0
  480. y'' *(y-1)-4x^2-4x-1 =0
  481. y'' *(y-1)-x^2- 4 =0
  482. y'' *(2y-1)-x^2-4x-4 =0
  483. y'' *(2y-1)-4x^2-4x-1 =0
  484. y'' *(2y-1)-x^2- 4 =0
  485. y'' *(2y-1)-4x-4 =0
  486. y'' *(2y-1)-x^2 =0
  487. y'' *(2y-1)-x =0
  488. y'' *(y-x-1)-x^2-4x-4 =0
  489. y'' *(y-x-1)-4x^2-4x-1 =0
  490. y'' *(y-x-1)-x^2- 4 =0
  491. y'' *(y-2x-1)-x^2-4x-4 =0
  492. y'' *(y-2x-1)-4x^2-4x-1 =0
  493. y'' *(y-2x-1)-x^2- 4 =0

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

  498. y''^2+x^2*y''-2y=0
  499. y''^2+x^2*y''-2y=1
  500. y''^2+x^2*y''-2y=2
  501. y''^2+2x^2*y''-4y=0
  502. y''^2+2x^2*y''-4y=1
  503. y''^2+2x^2*y''-4y=2

    Third order ode

    It cannot seem to solve the high order nonlinear ODE.

  504. y''' -y^2 =0
  505. y''' -y^3 =0
  506. y''' -y^4 =0
  507. y''' -y^5 =0
  508. y''' -y^n =0

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

  533. y''' -2y^2 =0
  534. y''' -3y^3 =0
  535. y''' -4y^4 =0
  536. y''' -5y^5 =0
  537. y''' -a*y^n =0

  538. y''' -1/y =0
  539. y''' -1/y^2 =0
  540. y''' -1/y^3 =0
  541. y''' -1/y^4 =0
  542. y''' -1/y^5 =0
  543. y''' -1/sqrt(y) =0
  544. y''' -1/cbrt(y) =0
  545. y''' = 1/exp(y)

  546. y''' -2y^2 *x =0
  547. y''' -3y^3 *x =0
  548. y''' -4y^4 *x =0
  549. y''' -5y^5 *x =0
  550. y''' -y^n *x =0

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

  552. y''' -2y^2 *x^2 =0
  553. y''' -2y^3 *x^2 =0
  554. y''' -2y^4 *x^2 =0
  555. y''' -y^5 *x^2 =0
  556. y''' -b*y^n *x^2 =0

  557. y'''-y^2-x^2 =0
  558. y'''-y^2-4x^2 =0
  559. y'''-y^2-x^4 =0
  560. y'''-y^2-4x^4 =0
  561. y'''-x*y^2-x^3 =0
  562. y'''-x^2*y^2-x^4 =0
  563. y'''-x*y^2-x^2* y=0
  564. y'''-x^2*y^2-x^3* y =0

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

  566. x*y''' -y* y' =0
  567. x^2*y''' -y* y' =0

  568. y''' -x *y* y' =0
  569. y''' -2x *y* y' =0
  570. y'''' -x *y* y'' =0
  571. y''' -x *y* y' =0

  572. y''' -x^2 *y* y'' =0
  573. y''' -x^3 *y* y'' =0
  574. y''' -x^2 *y* y'' =0

  575. y''' -sqrt(x) *y* y' =0
  576. y''' -sqrt(x) *y* y' =0

  577. y''' -x^2*y * y''' =0
  578. ......
  579. y''' -x^a *y* y''=0

  580. y'''-x^2*y'-x*y-x^2=0
  581. y'''-x^2*y'-x*y-2x^2=0
  582. y'''-x^2*y'-x*y-3x^2=0
    .......
  583. y'''-x^2*y'-x*y-c*x^2=0

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

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

  593. y''' -exp(x)*y^2=0
  594. ......
  595. y''' -exp(x)*y^2=0

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

  600. (x) *y''' - y^2=0
  601. (x) * y''' - y^2=0
  602. (x) * y''' - y^3=0
  603. ......
  604. (x) * y''' - y^p=0

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

  608. (x^n) *y''' - y^p=0
  609. ......
  610. (x^n)* y''' - y^p=0

  611. y''' -exp(x)*y*y'=0
  612. ......
  613. y''' -exp(x)*y*y'=0

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

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

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

  624. 3exp(x)*y''- y * y''' =0
  625. 4exp(x)*y''' - y * y'' =0
  626. ......
  627. a*exp(x) * y''' - y * y'' =0

  628. y'*y''' -x^2 =0
  629. y'*y''' -x^3 =0
  630. y'*y''' -x^4 =0
  631. y'*y''' -x^m =0
  632. y'*y''' -x-c =0
  633. y'*y''' -x^2 -b*x=0
  634. y'*y''' -a*x^2 -b*x-c=0
  635. y'*y''' -x*y =0
  636. y'*y''' -x^2*y^2 =0
  637. y'*y''' -x^m*y^n =0

  638. y^2*y''' -x^2=0
  639. y^2*y''' -x^3=0
  640. y^2*y''' -x^n=0

  641. y^2*y''' -(1+x)^2=0
  642. y^2*y''' -(2+x)^3=0
  643. y^2*y''' -(3+x)^n=0

  644. y^3*y''' -x^2=0
  645. y^3*y''' -x^3=0
  646. y^3*y''' -x^n=0

  647. y^m*y'' -x^n =0
  648. y^m*y''' -x^n =0

  649. y*y'*y''' =x
  650. y*y'*y''' =x^2
  651. y*y'*y''' =x^3
  652. y*y'*y''' =x^n

  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''' = exp(x)*y^2
  662. y''' = exp(x-1)*y^2
  663. y''' = exp(x-2)*y^2
  664. y''' = exp(x-3)*y^2
  665. y''' = exp(x-c)*y^2

  666. y''' = exp(x)*y^3
  667. y''' = exp(x-1)*y^3
  668. y''' = exp(2x-2)*y^3
  669. y''' = exp(x-3)*y^3
  670. y''' = exp(2x-c)*y^3
  671. y''' = exp(x)*y^m
  672. y''' = exp(a*x-b)*y^m

  673. y''' = exp(y-3x^2-3x-1)
  674. y''' = sqrt(y-3x^2-3x-1)
  675. y''' = cbrt(y-3x^2-3x-1)
  676. y''' = sin(y-3x^2-3x-1)
  677. y''' = sinh(y-3x^2-3x-1)

  678. y''' = exp(y-x^3-3x^2-3x-1)+6
  679. y''' = sqrt(y-x^3-3x^2-3x-1)+6
  680. y''' = cbrt(y-x^3-3x^2-3x-1)+6
  681. y''' = sin(y-x^3-3x^2-3x-1)+6
  682. y''' = tan(y-x^3-3x^2-3x-1)+6
  683. y''' = sinh(y-x^3-3x^2-3x-1)+6
  684. y''' = tanh(y-x^3-3x^2-3x-1)+6

  685. y'*y''' = exp(x)
  686. y'*y''' = exp(x-1)
  687. y'*y''' = exp(x-2)
  688. y'*y''' = exp(x-3)
  689. y'*y''' = exp(x-c)

  690. y'*y''*y''' = exp(x)
  691. y'*y'' = exp(x)*y'''
  692. y''*y''' = exp(x)*y'
  693. y'*y''' = exp(x)*y''
  694. y''' = exp(x) *y' *y''
  695. y''' = exp(x) *y' *y
  696. y''' = exp(x) *y'' *y
  697. y''' = exp(x+y)
  698. y''' = exp(x)*y'
  699. y''' = exp(x)*y''

  700. y''' = exp(y)
  701. y''' = exp(y-1)
  702. y''' = 2exp(y)
  703. y''' = 3exp(y-1)
  704. y''' = y' exp(y)
  705. y''' = y'' exp(y)
  706. y''' y' = exp(y)
  707. y''' y''= exp(y)
  708. y''' = exp(y)
  709. y''' = a *exp(y+c)
  710. y''' = y' *exp(y+c)
  711. y'''* y'' = exp(y+c)

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

  736. y* y'''-x^n =0
  737. y* y'''-2x^n =0
  738. y* y'''-3x^n =0
  739. y* y'''-a*x^n-b*x-c =0

  740. y*y'''-y^3-x^2 =0
  741. y*y'''-y^3-4x^2 =0
  742. y*y'''-y^3-x^4 =0
  743. y*y'''-y^3-4x^4 =0
  744. y*y'''-x*y^3-x^3 =0
  745. y*y'''-x^2*y^3-x^2 =0
  746. y*y'''-x*y^3-x^4=0
  747. y*y'''-x^2*y^3-x^6=0
  748. y*y'''-x*y^3-4x^3 =0
  749. y*y'''-x^2*y^3-4x^2 =0
  750. y*y'''-x*y^3-4x^4=0
  751. y*y'''-x^2*y^3-4x^6=0

  752. y*y''' -x -y' =0
  753. y*y''' -2x -y' =0
  754. y*y''' -x -2y' =0
  755. y*y''' -4x -2y' =0

  756. y*y''' -x -y''*x =0
  757. y*y''' -2x -y''*x =0
  758. y*y''' -x -2y''*x =0
  759. y*y''' -4x -2y''*x =0

  760. y'''+y* y''-3x^2-3x-1=0
  761. y'''+y* y''-3x^2-1=0
  762. y'''+y* y''-x^2-b*x-c =0
  763. y'''+y* y''-x^2-b*x =0
  764. y'''+y* y''-x^2-c =0
  765. y'''+y* y''-a*x^2-b*x-c =0
  766. y'''+y* y''-a*x^2-b*x =0
  767. 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.
  768. y*y'''' -x^2=0
  769. y*y'''' -x^3=0
  770. y*y'''' -x^n=0
  771. y*y'''' -(1+x)^2=0
  772. y*y'''' -(2+x)^3=0
  773. y*y'''' -(3+x)^n=0
  774. y*y'''' -a*x^4-b*x^3-c*x^2-d*x-f =0

  775. y'*y'''' -x^2 =0
  776. y'*y'''' -x^3 =0
  777. y'*y'''' -x^4 =0
  778. y'*y'''' -x^m =0
  779. y'*y'''' -x^2 -4x-4=0
  780. y'*y'''' -x^3 -b*x^2-c*x=0
  781. y'*y'''' -a*x^3 -b*x^2-c*x+f=0
  782. y'*y'''' -x*y =0
  783. y'*y'''' -x^2*y^2 =0
  784. y'*y'''' -x^m*y^n =0

  785. y''*y'''' -x^2 -b*x-c=0
  786. y''*y'''' -x^2-c*x=0
  787. y''*y'''' -x-c =0
  788. y''*y'''' -b*x^2-c*x+f=0
  789. y''*y'''' -x^2*y^2 =0
  790. y''*y'''' -x^m*y^n =0

    ... ...

    fractional order

  791. if the order of all these equations changed to fractional order, wolfram cannot solve too.
  792. It cannot solve fractional calculus
  793. fractional order differential equations,
  794. pi-order differential equations,
  795. negative order differential equations,
  796. complex order differential equations,
  797. variable order differential equations
  798. fractional order integral equations,
  799. double integral equations,
  800. fractional order partial integral equations,
  801. complex order partial differential equations,
  802. Equation of mixed Fractional differential and integral orders
  803. Equation of mixed Fractional partial differential and integral orders

    partial differential equation

  804. if adding a term to above equations become the partial differential equations, wolfram has the same problem.
  805. high order partial differential equations
  806. 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: 
See Also