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Homework Help: Laplace transform w/ partial fraction

  1. Dec 10, 2006 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant 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)


    3. 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!
     
  2. jcsd
  3. Dec 10, 2006 #2

    benorin

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    Homework Helper

    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.
     
  4. Dec 10, 2006 #3
    thanks a lot!
     
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