Hi. Im a bit stuck on the following question: 'Find the general solutions of....

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

So Ive rearranged it as usual and seperated the variables to get:

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

If dy and dx were not squared, I would know what to do. But what do I do now that theyre squared?

2. Originally Posted by Croc
Hi. Im a bit stuck on the following question: 'Find the general solutions of....

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

So Ive rearranged it as usual and seperated the variables to get:

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

If dy and dx were not squared, I would know what to do. But what do I do now that theyre squared?

Take the square root of both sides.

3. The DE can be written as...

$\displaystyle \frac{dy}{dx} = \frac{y^{2}}{x^{2}}\cdot \frac{dx}{dy}$ (1)

... and if we multiply both terms of (1) by $\displaystyle \frac{dy}{dx}$ we obtain...

$\displaystyle y^{' 2} = \frac{y^{2}}{x^{2}}$ (2)

... or equivalently...

$\displaystyle y^{'} = \pm \frac{y}{x}$ (3)

The (3) is a complex of two first order DE and the solution of each of them is confortable enough...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$