- #1

real analyst

- 10

- 0

## Homework Statement

(ds/dy)=(y+2s)/(y-2s)

## Homework Equations

## The Attempt at a Solution

I let V= s/y and this gave me *(ds/dy)=(1+2V)/(1-2V)

Then because V= s/y I said s=Vy and (ds/dy)=V + y(dV/dy)

Right so then my equation looked like V + y(dV/dy)=(1+2V)/(1-2V)

and then obviously I could do this : y(dV/dy)=(1+2V)/(1-2V) - V

then because I wanted to make V part of the quotient so It becomes

(1+V+2V^2)/(1-2V) = y(dV/dy)

now this is a separable equation, so I can transform it to

(dy/y)= (1-2V)(dV)/(1+V+2V^2) so, integrating both sides gives me LN|y|= the integral of the right side, but, how do you do this? this is where I get lost. I think the answer might be that (1+2V)/(1-2V) can be re written in a simplified way buit I can't remember it. Plz help.