how do you separate these variables dy/dx=4sqrt(y)lnx/x, y(e)=9

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  1. use the fact that
    integral dy/dx dx = integral dy = y
    find the antiderivative and plug in e and 9 to solve for the constant... i think...

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  2. dy/y^.5 = 4 ln x /x

    2 y^.5 = 2 (ln x)^2

    y^.5 = (ln x)^2 + C

    y = (ln x)^4 + c

    (e, 9) is on it
    9 = 1^4 + c
    c = 8
    y = (ln x)^4 + 8

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