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I am solving a heat equation in following example:

heqn = D[u[x, t], t] == D[u[x, t], {x, 2}];
ic = u[x, 0] == Exp[-x^2];
sol = DSolveValue[{heqn, ic}, u[x, t], {x, t}]

I'd like to manipulate the solution by plotting it in space for a given time. However a naive way of implementing it gives an empty plot:

Manipulate[
 Plot[sol, {x, -2, 2}, PlotRange -> All],
 {t, 0, 1}
]

What is a proper way of using Manipulate in such a case?

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1 Answer 1

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This is a classic pitfall in localization by Manipulate. I'll try to find a similar Q&A.

heqn = D[u[x, t], t] == D[u[x, t], {x, 2}];
ic = u[x, 0] == Exp[-x^2];
sol[x_, t_] = DSolveValue[{heqn, ic}, u[x, t], {x, t}]

Manipulate[
 Plot[sol[x, t], {x, -2, 2}, PlotRange -> All],
 {t, 0, 1}
]
Improve this answer
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