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 AM #1

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## 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?

- Dec 15th 2010, 07:18 AM #2
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 AM #3

- Dec 15th 2010, 07:58 AM #4

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- Nov 2010
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