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Math Help - First Order Differential Equation

  1. #1
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    First Order Differential Equation

    find the general solution of the first order differential equation, t2 y 2 ty = 3
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by winsome View Post
    find the general solution of the first order differential equation, t2 y’ – 2 ty = 3
    I'm assuming you mean t^2y^{\prime}-2ty=3.

    First note that this is the same thing as saying y^{\prime}-\frac{2}{t}y=\frac{3}{t^2}.

    Now this is a first order linear DE. Do you know how to proceed using the integrating factor method?
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  3. #3
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    i got integrating factor of this equaiton is t^-2
    is that is right ?
    if yes then i m unable to get its final answer
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  4. #4
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    Yes it's right.

    So multiply both sides by the integrating factor to get

    \displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}

    \displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}.


    You should be able to go from here.
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  5. #5
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    thanks
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  6. #6
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    Quote Originally Posted by Prove It View Post
    Yes it's right.

    So multiply both sides by the integrating factor to get

    \displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}

    \displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}.


    You should be able to go from here.

    thanks for providing solution
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