I am stuck trying to solve this equation using Laplace transform:
$$ y''(t)+2y(t)=\displaystyle 3\int_0^t (t−u)y(u)du\\ y(0)=2 , y'(0)=3 $$
I got stuck after performing the Laplace transformation and can't get the equation to a form I can do the inverse Laplace transformation on.
Here's what I got:
$$p^2Y(p)- py(0)-y'(0) + 2Y(p) = 3/p^2 * Y(p) $$ which then simplifies to: $$ Y(p) = (2p+3)/(p^2-3/p^2 +2)$$
How can I do inverse Laplace on this?
Thank you