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Bug introduced in 11.2 or earlier, fixed in 12.2 or earlier.

Reported to Wolfram with CASE number 4028951

on 11.3,

ClearAll[u,x,t];
eqn=D[u[x,t],t]+u[x,t]*D[u[x,t],x]==0;
bc=u[0,t]==0;
ic=u[x,0]==x;
sol=DSolve[{eqn,bc,ic},u[x,t],x,t]

Mathematica graphics

What does, terms that have

     DSolve`DsolveLaplaceTransformDump`

mean in the solution? It looks like DSolve starting using the Laplace method to solve the above PDE. But is the above answer meant to be the final answer, or did DSolve gave up in the middle and these Dump messages are left there?

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  • 1
    $\begingroup$ It's a context that's used by internal functions. Usually, the answer is rewritten in terms of user variables. Happens on 11.2, too. I don't think it should happen. $\endgroup$
    – Michael E2
    Mar 12, 2018 at 13:54
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    $\begingroup$ That's a bug, please report it. The Dump context should never leak. $\endgroup$
    – user21
    Mar 12, 2018 at 13:56

1 Answer 1

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The bug is fixed in v12.2 or earlier, now DSolve returns unevaluated:

enter image description here

It's a bit sad that DSolve still cannot solve the problem.

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