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Math Help - first order DE

  1. #1
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    first order DE

    Which method do I use to solve

    (1 + t^2) dy/dt + 2ty = -picos(pi*t) y(0) = 0

    I couldn't find a method to match this DE
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  2. #2
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    Well I don't if you can see it or not, but the LHS says this

    ay'+a'y = ay (product rule)

    since d/dt(1+t^2) = 2t and y->y'

    we can say LHS = (1+t^2)*y = -pic0s(pi*t)

    then y=-picos(pi*t)/1+t^2

    or you can simply use the p(x)=e^int(something)
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  3. #3
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    I think you actually mean

    ay' + a'y = \frac{d}{dt}(ay).

    So that means

    \frac{d}{dt}[(1 + t^2)y] = -\pi \cos{(\pi t)}.

    Go from here.
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