Thread: 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?

Originally Posted by Mcoolta

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

Yes, it is correct, but the substitution is better. You will obtain a separated variables equation.

Fernando Revilla

The original DE is also Bernoulli.

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