# Thread: dy/dx = (y^2 - x^2)/xy

1. ## dy/dx = (y^2 - x^2)/xy

I need to find the general solution, in explicit form of this equation:

dy/dx = (y^2 - x^2)/xy

Let u = xy

y =u/x

du/dx = y + dy/dx

So i then get;

du/dx - (u/x) = [(u/x)^2 - x^2]/u

Is this correct so far? Could anyone tell me where to go next?

2. Originally Posted by Mcoolta
Is this correct so far? Could anyone tell me where to go next?
Yes, it is correct, but the substitution $y=ux$ is better. You will obtain a separated variables equation.

Fernando Revilla

3. The original DE is also Bernoulli.

4. Ok so using y = ux

dy/dx = x(du/dx) + u

x(du/dx) + u = [(ux)^2 - x^2]/x^2u

After rearranging, i got

X(du/dx) = -1/u

Then:

1/x dx = -u du

Is this correct? Thanks