The laplace transform for ramp function with a time delay can be expressed as follows
Step 1
Let the time delay is T,
So the ramp function will be
Where
Step 2
Let the Laplace transform of f(t) is F(s)
So the Laplace transform is
let
x=t-T
So we have
y''-2y'-3y=0 for y(0)=3, y'(0)=2