Homogeneous differential equation - serious help

[masterchiefo]

Homework Statement

I need to resolve this with v = y/x

dy/dx= (3y²-x²)/(2xy)

Homework Equations

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 ?

 

[andrewkirk]

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

 

[masterchiefo]

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

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

 

[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.

 

[masterchiefo]

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.

what do you mean by left hand side ?

 

[andrewkirk]

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

 

[masterchiefo]

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

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.

 

[HallsofIvy]

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