solve y"+4y-4z'=3x

Question

z"+z-y'=1-x
where y(0)=z(0)=1
and y'(0)=z'(0)=0
by laplace transform

Answer 1

no ideas?

Recall that
L{y} = F(s)
L{y'} = s F(s) - f(0)
L{y"} = s^2 F(s) - s f(0) - f'(0)

then just collect terms, solve for s, and do L^-1{s}