Integrating factors round 2

  • Thread starter ssb
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  • #1
ssb
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Homework Statement



[tex]y' (1+e^t) + e^ty = 0[/tex]

How do I get it in the form

[tex]y' +f(t)y = f(p) [/tex]

That is how do apply algebra to this so it is in the proper form to process it?

The Attempt at a Solution



Kind of hard to post my attempt. I can move the y' (1+e^2) to the right side then divide both sides by y' but that doesn't make it y' + something, rather y' x something.

I also tried moving everything to the right and canceling some stuff out but it doesnt seem to work.
 
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Answers and Replies

  • #2
Dick
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Divide both sides by (1+e^t). Then read off f(t). What's f(p)????
 
  • #3
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Try dividing throughout by [itex](1+e^t)[/itex].
 
  • #4
ssb
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Divide both sides by (1+e^t). Then read off f(t). What's f(p)????

[tex]f(p)[/tex] becomes

[tex](e^ty)/(1+e^t)[/tex]

giving equation


[tex]y' + (e^ty)/(1+e^t) = 0[/tex]

Are you saying it is allowed to do this step even though the right hand side is zero? I always thought this was a no-no.
 
  • #5
Dick
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You aren't dividing by the RHS. You're dividing by (1+e^t). I'm still bothered by what 'p' is supposed to be. You've got f(t)=e^t/(1+e^t) alright.
 
  • #6
ssb
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You aren't dividing by the RHS. You're dividing by (1+e^t). I'm still bothered by what 'p' is supposed to be. You've got f(t)=e^t/(1+e^t) alright.

Gotcha. Thankyou so much. I got messed up a few weeks ago when I was given an assignment by my teacher with the wrong answer key. This is now going well. Thankyou thankyou! Thankyou
 

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