Solving a Separable ODE: y'+ytanx=cosx with Initial Condition y(0)=1

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Homework Help Overview

The problem involves solving a separable ordinary differential equation (ODE) of the form y' + y tan(x) = cos(x) with the initial condition y(0) = 1. The discussion centers around the methods for solving this type of equation and the application of integrating factors.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the method of integrating factors and expresses confusion about their progress. They question whether they are on the right track with their calculations and the simplification of the integrand.

Discussion Status

Some participants provide feedback on the original poster's calculations, indicating that they are on the right track. There is a discussion about the simplification of the integrand, with one participant confirming the correctness of an algebraic manipulation. The conversation reflects an ongoing exploration of the problem without a clear resolution.

Contextual Notes

Participants are navigating the constraints of the homework context, including the requirement to use specific methods for solving ODEs and the initial condition provided.

eeriana
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Homework Statement


y'+ytanx = cos x y(0)=1


Homework Equations





The Attempt at a Solution



We are studying separable ode's and integrating factor right now, I am a little confused... If someone could steer me in the right direction, it would be greatly appreciated... This is what I have so far:

P= tanx
\intP = -ln|cosx|
\mu=e^{}-lncosx
\mu= 1/cosx

(1/cosx*y)' =\int1/cosx cosx

and this is where I get stuck... am I even on the right track?

Thanks

Eeriana
 
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You are on the right track and have calculated the IF correctly and written the complete differential correctly. Note that you can simplify the integrand...
 
But isn't 1/cosx * cosx = 1 Or am I having an algebraic malfunction?
 
eeriana said:
But isn't 1/cosx * cosx = 1 Or am I having an algebraic malfunction?
Nope you are indeed correct.
 
I thought I was doing something wrong... hmmm..now I am going to see if I can finish it!

Thanks for the help
 

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