Final round: Integrating factors

[ssb]

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?
$$\frac{dy}{dt}=\frac{1}{t+y},\:y(-1)=0$$

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 $$\frac{dy}{dt}=\frac{1}{\frac{dt}{dy}}$$ but when I try to apply it to my initial equation, I get the same thing I started with.

 

[Dick]

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

 

[ssb]

'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 don't mean rename everything but just work the problem through solving for f(y) instead of y(t)?

Just fyi I love you.

 

[Dick]

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

Just fyi I love you.

Exactly...