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Math Help - fractured mixed equations 3 c

  1. #1
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    fractured mixed equations 3 c

    y''+(\frac{x}{1+x})y'+(\frac{1}{1+x})y=0
    for x>-1

    i dont know how to solve it
    i was told to find a solution by the form of y1=e^x

    and getting a solution

    how?
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  2. #2
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    If you multily by 1 + x then

    (1+x)y'' + xy' + y = 0. Now \dfrac{d}{dx}(xy'-y) = x y'' and \dfrac{d}{dx} (xy) = x y' + y.

    So, your original equation can be written as

    \dfrac{d}{dx} \left(y' + xy' - y + xy \right) = 0.

    Your turn!
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