# Laplace Transforms

by popo902
Tags: laplace, transforms
 P: 60 1. The problem statement, all variables and given/known data Im having trouble finding ways to manipulate equations to fit something from the table The two i'm stuck on are these 1. $\frac{1}{s^{2}- 2s + 3} (\frac{1+(s^{2}+1)e^{-3\Pi S}}{(s^{2}+1)})$ = Y(s) 2.$\frac{1}{s^{2}- 2s + 2} (\frac{s}{s^{2}+1} + s - 2)$ = Y(s) 2. Relevant equations These are the IVPs i got them from 1. y" - 2y' + 3y = sint + $$\delta$$(t - 3*pi) y(0) = 0 y'(0) = 0 2. y'' - 2y' + 2y = cost y(0) = 1 y'(o) = 0 3. The attempt at a solution I tried all sorts of things like multiplying the equations out i still can't seem to find a way to comfortably manipulate it to match anything on the laplace table can some one help or give me a tip?
 HW Helper P: 1,585 The first thing I would recommend to do is write: $$s^{2}-2s+3=(s-1)^2+2,\quad s^{2}-2s+2=(s-1)^2+1$$ Then I think the transform looks like a convolution doesn't it?
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,534 Use partial fractions to break them up.
HW Helper
P: 1,585

## Laplace Transforms

You can't use partial fractions here.
HW Helper
Thanks
P: 4,676
 Quote by hunt_mat You can't use partial fractions here.
Yes, you can. Some of the denominators remain quadratic in s if you restrict yourself to reals, but can be fully expanded out to linear factors if you use complex roots.

RGV
 P: 60 I see i see but how did you get the equations to look like that? and could you get the inverse laplace transforms with complex numbers??
Emeritus