# How to solve this partial differential equation?

I want to solve the following $$\frac{\partial^2 T}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial T}{\partial \rho}=\frac{1}{\alpha^2}\frac{\partial T}{\partial t}$$ with boundary conditions $$T(\rho, 0)=f(\rho) \qquad 0 \leq \rho \leq 1$$ and $$T(1,t)=0$$

Using Mathematica.

I tried

DSolve[D[T[r, t], {r, 2}] + (1/r)*D[T[r, t], r] = (1/a)*D[T[r, t], t], T[r, t], {r, t}]

but it gives me error.

• Use == instead of =. – J. M. will be back soon Apr 23 '17 at 12:56

PDE = D[T[r, t], {r, 2}] + (1/r)*D[T[r, t], r] == (1/a)*D[T[r, t], t];