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Solving a second order differential equation using Fourier s

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Consider the ODE

y" - a^2 * y = H(x-Pi/2)

y(0)=y(Pi)=0
0<x<Pi

Where H is the step function.

solve for y using Fourier series
The Fourier series for the step function exhibits the Gibss phenomenon. Will the solution y(x) exhibit it too? explain why or why not.

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https://brainmass.com/math/fourier-analysis/fourier-series-gibbs-phenomenon-235759

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