$$y''+3y'+2y=\cos(at) $$
where a is a constant. Find solution of this initial value problem in terms of convolution integral.$( y(0)=1$ and $ y'(0)=0 )$
I couldn't solve this problem with convolution integral. If somebody helps me, I'll appreciate.
I found: $$Y(s)=\dfrac 1 {s^2+3s+2} \left(\dfrac s {s^2+a^2}+s+3 \right)$$ with Laplace transformation.After this, I have to use convolution integral. When I use it, the integral becomes too difficult. Actually, I found the result of the integral but I think the result is wrong.