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Bug introduced in 8.0 or earlier and fixed in 10.3.0


I am solving With Mathematica 10 the following ODE system:

DSolve[{B'[x] == -f[x]*Cos[l]*G[x], G'[x] == +f[x]*Sin[l]*B[x]}, {B,G}, x]

The solution is almost trivial, but Mathematica gives me this expression:

enter image description here

What is

(* -DSolve`DSolveFirstOrderODEsDump`const$26192[2]*)

I can't find it in any tutorial online.

Is this a bug? I cannot check with another version...

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  • 3
    $\begingroup$ It's a bug. Just consider it to be a second constant parameter, C[2]. $\endgroup$ – ilian May 31 '15 at 17:16
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    $\begingroup$ Same in version 8 $\endgroup$ – uranix May 31 '15 at 17:28
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    $\begingroup$ @ilian Taking it as a second constant, this solution appears to be correct. But in version 10.2.0, DSolve returns unevaluated instead of returning this solution. Is that a separate, new-in-10.2 bug? $\endgroup$ – Szabolcs Jul 24 '15 at 19:23
  • $\begingroup$ @Szabolcs I've mentioned this to the developers and they will be looking into it. $\endgroup$ – ilian Jul 24 '15 at 20:19
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As of Mathematica 10.3, a solution is returned by DSolve

eqns = {B'[x] == -f[x]*Cos[l]*G[x], G'[x] == +f[x]*Sin[l]*B[x]};
sol = DSolve[eqns, {B, G}, x]

(* {{B -> 
   Function[{x}, 
    1/2 (-2 E^-Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1, x},
            Assumptions -> True] + E^
        Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1, x}, 
         Assumptions -> True]) C[1] + 
     1/2 E^(1 + 
       Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1, x}, 
        Assumptions -> True]) C[2]], 
  G -> Function[{x}, 
    1/2 I E^(
      1 + Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1, x}, 
        Assumptions -> True]) C[2] Sec[l] Sqrt[Cos[l] Sin[l]] - (1/(
     2 f[x]))C[1] Sec[
       l] (-2 I E^-Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1,
             x}, Assumptions -> True] f[x] Sqrt[Cos[l] Sin[l]] - 
        I E^Integrate[-I f[K[1]] Sqrt[Cos[l] Sin[l]], {K[1], 1, x}, 
          Assumptions -> True] f[x] Sqrt[Cos[l] Sin[l]])]}} *)

Simplify[eqns /. sol]

(* {{True, True}} *)
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  • $\begingroup$ Can you please take a look here? I think it's a bug that with the new DateString specifications only a single tick mark is shown in these examples. I don't want to send support requests about other people's problems, but I wanted to make sure that someone at WRI will notice ... $\endgroup$ – Szabolcs Oct 21 '15 at 12:23

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