Question

Consider the heat equation (∂u/∂t)=k(∂²u/∂x²), for t>=0, and x in [0,L] subject to the homogeneous boundary conditions (∂u/∂x)|ₓ=0=0, and u(L,t)=0. Solve the initial val
(a) Exponential decay
(b) Sine wave
(c) Gaussian distribution
(d) Linear growth