Explain the step function exhibits the gibss phenomenon

Question

Assignment:

Consider the ODE with boundary conditions

y" - a²y = H(x-Π/2); 0 ≤ x ≤ Π

y(0)=y(Π) = 0

Where H (x-c) is the step function:

H (x-c) = {0 x < c

              1 x > c}

(a) Solve for y(x) using Fourier series

(b) The Fourier series for H(x-Π/2) the step function exhibits the Gibss phenomenon. Will the solution y(x) also exhibit the global Phenomenon? Explain why or why not.