7
$\begingroup$

Bug introduced in 13.1. and fixed in V 13.2.1

Submitted to WRI. CASE ID [CASE:4975479].

I was looking at this question.

In V 13.1 I get an internal error which the above question does not mention so I assume it is a version difference? I slightly changed the input to make it more clear:

ClearAll[r, x, u]
ode1 = r''[x] + r[x] * (u'[x])^2 == 0
ode2 = u''[x] * r[x] + 2 * r'[x] * u'[x] == 0
ic = {r[0] == 1, r'[0] == 0, u[0] == 0, u'[0] == 0}

And now

DSolve[{ode1, ode2, ic}, {r[x], u[x]}, x]

gives

Mathematica graphics

Why this error generated? Is this a bug? I see nothing wrong with the input. Does this happen on other versions/systems?

V 13.1 on windows 10.

Improve this question
$\endgroup$
5
  • 2
    $\begingroup$ Cannot reproduce it in version 13.0.1 for Linux x86 (64-bit) (January 29, 2022) $\endgroup$
    – mattiav27
    Commented Oct 11, 2022 at 8:46
  • 2
    $\begingroup$ In v12.0.0 Windows10 DSolve doesn't evaluate, perhaps because {ode1, ode2} /. x -> 0 /. (ic /. Equal -> Rule) gives {r''[0] == 0, u''[0] == 0} $\endgroup$
    – Ulrich Neumann
    Commented Oct 11, 2022 at 9:48
  • 2
    $\begingroup$ Version 13.1 Windows 10 produces this error. As the same equations with NDSolve work, I think it is a bug. Please report it to [email protected] $\endgroup$
    – Daniel Huber
    Commented Oct 11, 2022 at 11:33
  • 2
    $\begingroup$ This is a confirmed bug. Interestingly I encountered this bug about 3 months ago when solving almost the same problem (asked in Chinese community). $\endgroup$
    – xzczd ♦
    Commented Oct 11, 2022 at 16:44
  • 2
    $\begingroup$ Fixed in 13.2.0. $\endgroup$
    – Валерий Заподовников
    Commented Dec 19, 2022 at 0:00

2 Answers 2

Reset to default
6
$\begingroup$

It's because DSolve`DSolveFirstOrderODEsDump`DSolvenOrder1NonlinearODEs has not been updated to pass DSolve`DSolveParser[] complete option value data (with the new options like IncludeSingularSolutions).

As far as I can tell, DSolve proceeds merrily along despite the error. All the error does is set a non-True value to DSolve`$DSolveSingularSolutions.

Similar issue here with another internal function: Why is DSolve unable to solve this second order ode with initial conditions? Any workaround?

FWIW, here's a general solution that DSolve generates internally for r and u' (not u). But DSolve rejects it, it seems, even though one can solve for u from u'. The IVP cannot be solved, however.

sol = # /.
      r -> 
       Function[{x}, 
        Sqrt[-C[1]^2 + 4 x^2 C[2]^2 - 8 x C[2]^2 C[3] + 
         4 C[2]^2 C[3]^2]/(Sqrt[2] Sqrt[C[2]])] /.
     u -> (Derivative[-1][v][#] + C[4] &) /.
    v -> 
     Function[{x}, (
      2 C[1] C[2])/(-C[1]^2 + 4 x^2 C[2]^2 - 8 x C[2]^2 C[3] + 
       4 C[2]^2 C[3]^2)] &;

{ode1, ode2} // sol // Simplify
(*  {True, True}  *)

u[x] // sol // Simplify
(*
1/2 (2 C[4] - Log[C[1] + 2 C[2] (x - C[3])] + 
   Log[C[1] + 2 C[2] (-x + C[3])])
*)

{r[0] == 1, r'[0] == 0, u[0] == 0, u'[0] == 0} // sol // 
  Simplify // Solve
(*  {}  *)
Improve this answer
$\endgroup$
2
  • $\begingroup$ DSolvenOrder1NonlinearODEs looks like a typo, but if so, WRI let it slide through. $\endgroup$
    – Michael E2
    Commented Oct 11, 2022 at 17:22
  • $\begingroup$ Compare with the numeric ode1 = r''[x] + r[x]*(u'[x])^2 == 0 ode2 = u''[x]*r[x] + 2*r'[x]*u'[x] == 0 ic = {r[0] == 1, r'[0] == 0, u[0] == 0, u'[0] == 0} sol = NDSolve[{ode1, ode2, ic}, {r[x], u[x]}, {x, 0, 1}]. $\endgroup$
    – user64494
    Commented Oct 11, 2022 at 17:31
1
$\begingroup$

This is fixed in V 13.2.1 as this screen shot shows

Mathematica graphics

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.