Using Laplace Transforms to solve IVP's

[dm59]

Homework Statement

solve the ivp using laplace tranforms

y''+2y'+2y=0 y(0)=1 y'(0)=-3

Homework Equations

The Attempt at a Solution

get to Y(s)[s^2+2s+2]=s-1

Y=(s-1)/[s^2+2s+2]

^^^
don't know how to simplify the denominator to solve using Laplace transforms. If I had to guess I would say maybe partial fractions but keep getting the wrong answer when I try to use them.

 

[jeffreydk]

You've pretty much finished it, all you need to recognize that

$$Y(s)=\frac{s-1}{(s-1)^2+1}$$

through completing the square in the denominator. Now can you get that to work with

$$f(t)=L^{-1}\left\{\frac{s-a}{(s-a)^2+b^2} \right\} = e^{at}\cos{(bt)}$$