Use the Laplace transform to solve the following initial value problem

Question

Use the Laplace transform to solve the following initial value problem:

y" - 4y' +29y = 0 y(0) = 0, y'(0) = 5

I have found the equation

s^2Y - s:0 - 5 - 4(sY - 0) + 29Y = 0

I know y(t) is e^(2t)sin(5t)

I need to find what Y(s) is

Answer 1

Y(s) = 5/(s² - 4s + 29) = 5/{ (s-2)² + 25) } = 5/{ (s-2)² + 5²) }

Then

y(t) = e^2tsin(5t)