# Math Help - simple differential equation with trig functions

1. ## 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

2. ## Re: simple differential equation with trig functions

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