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Math Help - [SOLVED] Can Anyone help solve this one?

  1. #1
    MB1380
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    [SOLVED] Can Anyone help solve this one?

    Any help appreciated
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    part i:

    y''+6y'+8y=40

    p^{2}Y-py(0)-y'(0)+6(pY-y(0))+8Y=\frac{40}{p}

    Using the initial conditons y'(0)=0 and y(0)=0:

    Y(p^{2}+6p+8)=\frac{40}{p}

    Y=\frac{5}{p+4}-\frac{10}{p+2}+\frac{5}{p}

    Use the inverse Laplace for each and get:

    y=5e^{-4t}-10e^{-2t}+5
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