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?

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- Dec 15th 2010, 06:11 AMMcooltady/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? - Dec 15th 2010, 07:18 AMFernandoRevilla
Yes, it is correct, but the substitution $\displaystyle y=ux$ is better. You will obtain a separated variables equation.

Fernando Revilla - Dec 15th 2010, 07:19 AMAckbeet
The original DE is also Bernoulli.

- Dec 15th 2010, 07:58 AMMcoolta
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