Differential equations w/ trig

b200w
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Okay this is the second time writing this out, hopefully it won't log me out again...

Given:
dy/dx = (e^y * sin^2(x))/(y*sec(x))

I separated out and integrated the y side using parts (for brevity's sake I won't repeat the math here as it's straightforward and presumably correct). I currently have this:

-(y+1)/e^y = INT[ sin^2(x)/sec(x) dx ]

My problem is I've never been able to completely grasp trig relations and I'm probably just missing something obvious but I spent an hour combing my book and previous homework assignments and I can't find a clue where to start. If someone could point me in the right direction I'll presumably be off and running. How would I integrate the RHS of the equation?
 
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1/sec(x) = cos(x) -- does that help?
 
So substitution yields sin^3(x)/3 then? Now it's just a question of isolating y on the other side... wish me luck hahaha! Thanks!
 
Yeah the integration looks right.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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