Consider the following initial value problem: $y′′−4y′−45y=\sin(3t)y(0)=5$, $y′(0)=3$. How can we find the equation obtained by taking the Laplace transformation in terms of $Y(s)$?
Here is where i got to but i dont know how to finish the question to get the answer. please help give the correct answer:
$Y(s) = s/[(s² + 9)(s² - 4s - 45)] + (5s - 17)/(s² - 4s - 45)$