Thread: Laplace transform stuff

the problem is: 4y'' + 4y' + 17y = g(t); y(0)=0 , y'(0)=0

I get Y(s)=G(s)/(4s^2 + 4s + 17) ... not sure how break up the bottom... i tried doing something like (2s+1)^2 + 4^2 ... but then i dont know how to account for the 2 in front of the "s" to make it similar to the form b/((s-a)^2 + b^2) ... any thoughts?

Originally Posted by diff'eq_austin

the problem is: 4y'' + 4y' + 17y = g(t); y(0)=0 , y'(0)=0

I get Y(s)=G(s)/(4s^2 + 4s + 17) ... not sure how break up the bottom... i tried doing something like (2s+1)^2 + 4^2 ... but then i dont know how to account for the 2 in front of the "s" to make it similar to the form b/((s-a)^2 + b^2) ... any thoughts?

I would factor the 4 out of the denominator first. Then you have to work with . Now do a partial fraction decomposition. Set . Once you do that, you should be able to do the inverse transform.

-Dan