Given g(t)= 4t for 0<t<1 and 4 for t>1 ;

Also given that L(g(t))= 4s^-2(1-e^-s)

Using this result solve

y''-4y=g(t) for y(0)=y'(0)=0

I first started it off like this

Let F(s)= y(t)

then,

s^2F(s)-4F(s)=4s^-2(1-e^-s)

F(s)=4s^-2(1-e^-s) / (s^2 -4)

I'm just having trouble separting the right hand side before finding it's inverse.

Thanks