Differential equations w/ trig

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Homework Help Overview

The discussion revolves around a differential equation involving trigonometric functions and exponential terms. The original poster attempts to integrate both sides after separating variables but expresses uncertainty regarding the integration of the right-hand side, which involves trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on integrating the right-hand side of the equation, specifically questioning their understanding of trigonometric relations. Some participants offer insights into trigonometric identities and suggest substitution methods.

Discussion Status

Participants are actively engaging with the problem, with some confirming the correctness of the integration steps taken by the original poster. There is a sense of progress as substitution methods are discussed, although no consensus on the final steps has been reached.

Contextual Notes

The original poster mentions a lack of clarity regarding trigonometric relations, indicating potential gaps in foundational understanding that may affect their approach to the problem.

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.
 

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