Describe the diffrence between the following two problems and give an example of a physical situation which may be modeled by each equation

Question

$y'' + y =\mu_\pi \big(t\big)$

$y''+y= \delta (x- \pi )$

wih initial conditions:

$y \big(0\big) =0$

$y' \big(0\big) =0$

It is obvious to me that the first equation is a Heaviside distribution and the second is a dirac delta funtion. I am not sure if that is the difference between them or I need to perform Laplace transforms to see the difference. Also I am not sure of any physical situation which would describe these eqautions. Any help would be greatly appreciated.