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Exceed time limit of trial plan while using DSolve in Wolfram cloud?

Posted 1 year ago

Can anyone tell me what is the output using advanced plan?

DSolve[(-2 - 2 x) t'[x] == 
  t[x] - t[x]^3 + (1 + x) t[x]^5 - (1 + x)^2 t[x]^7, t[x], x]
POSTED BY: SHAOXUAN HUANG
4 Replies
dsolYU = DSolveChangeVariables[
  Inactive[DSolve][(-2 - 2 x) t'[x] == 
    t[x] - t[x]^3 + (1 + x) t[x]^5 - (1 + x)^2 t[x]^7, t, x], y, u, 
  x == u - 1] // Activate

quickly returns the implicit solution

Solve[Log[y[u]] + 
   1/12 (6 Log[u] - 
      I (-3 I + Sqrt[3]) Log[I + Sqrt[3] - 2 I u y[u]^2] + 
      I (3 I + Sqrt[3]) Log[-I + Sqrt[3] + 2 I u y[u]^2] + (
      6 (-1 + y[u]^2))/(u y[u]^2)) == C[1], y[u]]

You may transform it back with

dsol = dsolYU /. {Solve -> Inactive[Solve], y[u] -> t[x], u -> x + 1}

to get

Inactive[Solve][
 Log[t[x]] + 
   1/12 (6 Log[1 + x] - 
      I (-3 I + Sqrt[3]) Log[I + Sqrt[3] - 2 I (1 + x) t[x]^2] + 
      I (3 I + Sqrt[3]) Log[-I + Sqrt[3] + 2 I (1 + x) t[x]^2] + (
      6 (-1 + t[x]^2))/((1 + x) t[x]^2)) == C[1], t[x]]

Be careful: The Solve[..] returned by DSolve appears to have been Defer[]-ed. If you use % or let the Solve evaluate, it won't finish even for a very long time, if ever.

POSTED BY: Michael Rogers

Thank you so much!

POSTED BY: SHAOXUAN HUANG

If I put this code to Mathematica 13.1, I abort the computation within 30 minutes.

Maple 2022.1 give me an answer in implicit form with about 1 sec.

enter image description here

POSTED BY: Mariusz Iwaniuk

I really appreciate your help for several questions I have posted. Thanks!

POSTED BY: SHAOXUAN HUANG
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