# Homogeneous differential equation - serious help

1. Sep 26, 2015

### masterchiefo

1. The problem statement, all variables and given/known data
I need to resolve this with v = y/x

dy/dx= (3y2-x2)/(2xy)

2. Relevant equations

3. The attempt at a solution
dy/dx= (3y2-x2)/(2xy)

dy/dx= 3y2/2xy -x2/2xy

dy/dx = 3y/2x -x/2y

dy/dx = 3y/2x - 1/2y/x

dy/dx = 3/2 *v - 1/2*v

F(v) = 3/2 *v - 1/2*v

is that good so far ?

Last edited: Sep 26, 2015
2. Sep 26, 2015

### andrewkirk

The First term in your 2nd line is wrong, and the error propagates through from there.

3. Sep 26, 2015

### masterchiefo

sorry I made a mistake in the original equation and now its fixed.
it was 3y3 but its actually 3y2

4. Sep 26, 2015

### andrewkirk

You've expressed the right-hand side in terms of v, so that's progress. Now you need to do similar work on the left hand side.

Using $v=\frac{y}{x}$, express $\frac{dv}{dx}$ in terms of y, y' and x, then see if you can use that to express y' in terms of v, v' and x. Equate that to the RHS and then with any luck you'll be able to use separation of variables to get an expression to be integrated over x on one side and the same for v on the other.

5. Sep 26, 2015

### masterchiefo

what do you mean by left hand side ?

6. Sep 26, 2015

### andrewkirk

LHS of the diff equation in section 1 of your OP, which is: $\frac{dy}{dx}$.

7. Sep 26, 2015

### masterchiefo

hey man, thanks for your time and help, I was able to get it resolved and it matched the answer in my book.
you are awesome.

8. Sep 27, 2015

### HallsofIvy

Staff Emeritus
Please do NOT erase the original problem after it has been solved. Other people can learn from this.