Using Laplace Transforms to solve IVP's

  • Thread starter dm59
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  • #1
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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.
 

Answers and Replies

  • #2
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You've pretty much finished it, all you need to recognize that

[tex] Y(s)=\frac{s-1}{(s-1)^2+1}[/tex]

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

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

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