Question: Consider the partial differential equation (PDE) du 1 x E (0, 7), t> 0 t +1dr2' a. Assuming a solution of the form u(r.

Consider the partial differential equation (PDE) du 1 x E (0, 7), t> 0 t +1dr2' a. Assuming a solution of the form u(r. t) = X(x)T(t), find the general solution of the PDE which satisfies the boundary conditions u(0, t) = u(T, t) = 0 for all t> 0 b. Find the solution of the PDE which also satisfies the initial condition u(r.0) = 1 for all r E (0, T) %3D

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