Solve the initial value problem if temperature is initially

Question

The 1D heat equation

Explain the steps on how to solve the problem below:

Consider the heat equation    ∂u/∂t= k(∂²u/∂x²)      0≤x≤L   t>0

subject to the boundary conditions   u(0,t)=0  and  u(L,t)=0

Solve for the initial value problem if the temperature is initially

a. u(x,0) = sin(5πx/L)

b. u(x,0) = x

c. For part b, plot the solution at t=0, 0.1, 1