Solution of the IVP $\frac{\partial{u}}{\partial{t}}+\frac{\partial^2{u}}{\partial{x^2}}=0$.

Question

Given $\frac{\partial{u}}{\partial{t}}+\frac{\partial^2{u}}{\partial{x^2}}=0$ with $u(x,0)=\sin{\pi x}$.

I don't know how to derive a solution of it. But I just want a hint to move forward. Not a solution. Can anybody provide one hint? Also is it some form of the heat equation?

Answer 1

It's more of a backwards heat equation.

Hint: separation of variables, try $ u=X(x)T(t) $.