Laplace transform w/ partial fraction

[SpartanArt]

Homework Statement

solve the following initial value problem using Laplace transforms
y"+2y'+y=(8/3)cos(2t)-2sin(2t)
y(0)=1
y'(0)=7/3

Homework Equations

L[d^2y/dt^2]=s^2Y-sy(0)-y'(0)
L[dy/dt]=sY-y(0)
L[coswt]=s/(s^2+w^2)
L[sinwt]=w/(s^2+w^2)

The Attempt at a Solution

so far: Y={s^3+(13/3)s^2+(20/3)s+(40/3)}/{(s^2+4)(s^2+2s+1)}
need help turning denominator into partial fraction.
Thanks!

 

[benorin]

www.quickmath.com - powered by webMathematica: this site is very handy and will do algebra (factoring, simplify, partial fraction decomposition, expand), solve equations/inequalities (single or a system), plot equations/inequalities (single or a system), derivatives, definite or indefinite integrals, and do matrix arithmetic/inverses/determinants.

 

[SpartanArt]

thanks a lot!