Homogeneous differential equation - serious help

Homework Statement

I need to resolve this with v = y/x

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

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:

andrewkirk
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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.

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