Final round: Integrating factors

  • Thread starter ssb
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  • #1
ssb
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Homework Statement


Final round I promise!!!!

Is there some sort of trick that can be applied to the following equation so that it is easier to process?
[tex]\frac{dy}{dt}=\frac{1}{t+y},\:y(-1)=0[/tex]

The Attempt at a Solution



Somebody told me that the equation can be made easier by reinterpreting it with y as the independent variable and t as the dependent variable. I still have a vacant look about my face now as I did back then.

I know that [tex]\frac{dy}{dt}=\frac{1}{\frac{dt}{dy}}[/tex] but when I try to apply it to my initial equation, I get the same thing I started with.
 

Answers and Replies

  • #2
Dick
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'Somebody' is right. It turns the equation into 1/t'=1/(t+y). Or t'=t+y. That does look a bit simpler, right?
 
  • #3
ssb
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'Somebody' is right. It turns the equation into 1/t'=1/(t+y). Or t'=t+y. That does look a bit simpler, right?

Then you just solve it the normal way as if t' were y'? I dont mean rename everything but just work the problem through solving for f(y) instead of y(t)???

Just fyi I love you.
 
  • #4
Dick
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Then you just solve it the normal way as if t' were y'? I dont mean rename everything but just work the problem through solving for f(y) instead of y(t)???

Just fyi I love you.

Exactly........
 

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