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Math Help - 2nd ODE trivial solution help.

  1. #1
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    2nd ODE trivial solution help.

    The problem is
    x''+5x'+6x=3e^(-2t)+e^3t


    The homogeneous solution, that I solved is,
    x(h)=A(1)e^(-3t)+A(2)e^(-2t)

    my problem is when I split it to find the first particular solution, for 3e^(-2t)
    I assume
    x=B(1)e^-2t
    x'=-2B(1)e^-2t
    x''=4B(1)e^-2t

    I substitute into the original and get
    e^(-2t)[4B(1)-10B(1)+6B(1)]=3e^(-2t)

    which reduces too
    4B-10B+6B=3

    This is trivial

    any help would be greatly appreciated.

    Thank you
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  2. #2
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    Quote Originally Posted by Zigy221 View Post
    The problem is
    x''+5x'+6x=3e^(-2t)+e^3t


    The homogeneous solution, that I solved is,
    x(h)=A(1)e^(-3t)+A(2)e^(-2t)

    my problem is when I split it to find the first particular solution, for 3e^(-2t)
    I assume
    x=B(1)e^-2t
    x'=-2B(1)e^-2t
    x''=4B(1)e^-2t

    I substitute into the original and get
    e^(-2t)[4B(1)-10B(1)+6B(1)]=3e^(-2t)

    which reduces too
    4B-10B+6B=3

    This is trivial

    any help would be greatly appreciated.

    Thank you
    Try y_p = at e^{-2t}.
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