How Do I Integrate Factors in Round 2 to Achieve the Proper Form for Processing?

[ssb]

Homework Statement

$$y' (1+e^t) + e^ty = 0$$

How do I get it in the form

$$y' +f(t)y = f(p)$$

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 doesn't seem to work.

 

[Dick]

Divide both sides by (1+e^t). Then read off f(t). What's f(p)?

 

[bdeln]

Try dividing throughout by $(1+e^t)$.

 

[ssb]

Divide both sides by (1+e^t). Then read off f(t). What's f(p)?

$$f(p)$$ becomes

$$(e^ty)/(1+e^t)$$

giving equation


$$y' + (e^ty)/(1+e^t) = 0$$

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.

 

[Dick]

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.

 

[ssb]

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