- #1

_diego

- 2

- 0

## Homework Statement

I have a 2nd order diff. equation:

3y''(t) + 2y'(t) + 5y(t) = 3

with initial values: y'(0) = 1, y(0) = 0

## Homework Equations

After using Laplace transform I get:

Y(s) = (3 + 3s) / (s*[3s

^{2}+2s +5])

I believe it is correct, but even if it's not, what I'm interested in is how to solve this particular inverse laplace transform where I can't use partial fractions due to 3s

^{2}+2s +5 not having any roots.

## The Attempt at a Solution

I'm kind of stuck here, but maybe I could split the fraction like:

Y(s) = 3 / (s*[3s

^{2}+2s +5]) + 3 / ([3s

^{2}+2s +5])

but the problem would remain.

Thanks