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Math Help - simple differential equation with trig functions

  1. #1
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    simple differential equation with trig functions

    this is not a homework problem or anything- i'm just doing it for fun and would like to know why i'm not getting what the back of the book gets. it seems really simple. well here it is; just solving the diff eq:

    3(e^x)(tan(y)) dx = (1-(e^x))(sec^2(y)) dy

    so after rearranging and integrating i get

    3ln|1-(e^x)|+ ln|tan(y)| = c

    and the book has for a solution;

    tan(y)*((1-(e^x))^3) = c


    so i'm confused. how can i find out if these are equivalent? besides i don't even see how they have that for an answer
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  2. #2
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    Re: simple differential equation with trig functions

    oh...could it be they turned it from a natural log problem to exponential?
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