I'm trying to solve a simple PDE in Mathematica. I just can't get Mathematica to give me an explicit analytical solution. This is the code that I made and it basically repeats in the output what I have given in the input.

Below are my input and output. What am I doing wrong?

pde = D[u[z, t], {t, 1}] + const* D[u[z, t], {z, 2}] == 0
DSolve[pde, u[z, t], {z, t}]
(u^(0,1))[z,t]+const (u^(2,0))[z,t]==0
DSolve[(u^(0,1))[z,t]+const (u^(2,0))[z,t]==0,u[z,t],{z,t}]
  • $\begingroup$ yes, I have, but how do I know that is the wrong syntax? I've never used this part of Mathematica before. The DSolve doc was not very helpful, which I came here. $\endgroup$
    – seb
    Commented Nov 1, 2013 at 13:33
  • $\begingroup$ actually, I do not get any messages (I thought you meant the output). I'm running Mathematica 9. It does not give me any error messages. $\endgroup$
    – seb
    Commented Nov 1, 2013 at 13:45
  • 1
    $\begingroup$ reference.wolfram.com/mathematica/tutorial/… $\endgroup$ Commented Nov 1, 2013 at 13:54
  • 2
    $\begingroup$ The short answer is that mathematica can't solve the heat equation symbolically. NDSolve does though but you have to specify appropriate boundary conditions. i.e. (const=-1) sol = NDSolve[{D[u[z, t], t] - D[u[z, t], z, z] == 0, u[-1, t] == t, u[z, 0] == 0}, u, {z, -1, 1}, {t, 0, 1}]See this and therein references about the warning. $\endgroup$
    – gpap
    Commented Nov 1, 2013 at 14:02


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