Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y′′−4y′=δ(t−1) ,y(0)=5, y′(0)=0.
y″−4y′=δ(t−1),y(0)=5,y′(0)=0. find the laplace transform of the solution.

(i have found Y(s) as (e^-s +5*s -20)/(s^2-4s) but couldn't manage to obtain the solution y(t).)

And there is a third part of the Q:

c.Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=1.
if 0≤t<1,
y(t)=
if 1≤t<∞.​