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Math Help - Inverse Laplace Transform help

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    Inverse Laplace Transform help

    s2F(s) + sF(s) - 6F(s) = (s2+4)/(s2+s) Solve for L-1{F}

    Attempt:

    Simplified the equation to F(s) = (s2+4)/[s*(s+1)*(s+3)*(s-2)]

    Fraction Decomposition s2+4 = A(s+1)(s+3)(s-2) + B*s(s+3)(s-2) + C*s(s+1)(s-2) + D*s(s+1)(s+3)

    For s = 0 ----> -6A = 4 ----> A = -2/3

    For s = -1 ----> 6B = 5 ----> b = 5/6

    For s = -3 ----> -30C = 13 ----> C = -13/30

    For s = 2 ----> 30D = 8 ----> D = 4/15

    Inverses I get:

    A: -2/3

    B: 5/6 * e-t

    C: -13/30 * e-3t

    D: 4/15 * e2t

    ----> L-1{F} = -2/3 + 5/6 * e-t + -13/30 * e-3t + 4/15 * e2t where s > -3

    I think I have an error in my factoring, but I am not sure. Could anyone help me out with this?
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    Re: Inverse Laplace Transform help

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