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Math Help - [SOLVED] Differential equation

  1. #1
    Junior Member superman69's Avatar
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    [SOLVED] Differential equation

    Find the function that satisfies the differential equation
    and the condition .

    So first of all I found integration factor which is
    Then I plugged it in for the general solution formula.

    which came out to be

    y= 6dt+C

    then it came out to be

    +C

    then I plugged in the values and got C=1 but all the work done wasn't correct
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  2. #2
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    When you multiply by the integrating factor, the equation becomes
    e^{-t^{2}}\frac{dy}{dt}-2te^{-t^{2}}y=6t^{2}.
    Integrating, you get
    e^{-t^{2}}y=2t^{3}+C, so
    y=e^{t^{2}}(2t^{3}+C), etc. .
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