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Math Help - Help on a differential equation

  1. #1
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    Help on a differential equation

    Need to find the general solution q(t) of

    q''+ 6q'+ 9q = (t^2)*(e^(-3t))


    I think it goes of finding solution of the form P(t)*e^(-3t) with P polynomial of degree 4.

    But not totally sure how to continue.

    Thank you for your assistance.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by taurine330 View Post
    Need to find the general solution q(t) of

    q''+ 6q'+ 9q = (t^2)*(e^(-3t))
    solve the homogeneous.

    the characteristic equation is r^2+6r+9=0, so we have equal roots and the solution is q_h(t)=c_1e^{-3t}+c_2te^{-3t}.

    see my second link to find the particular solution.
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