$\displaystyle y\left( y^{3}\; -\; x \right)dx\; +\; x\left( y^{3}\; +\; x \right)dy\; =\; 0$
Can't seem to find the family of solutions...
Any ideas?
Finally got it!
Regroup the original equation to get:
$\displaystyle y^{3}\left( ydx\; +\; xdy \right)\; +\; x^{2}dy\; -\; xydx\; =\; 0$
or:
$\displaystyle y^{3}\left( xy \right)'\; +\; x^{2}dy\; -\; xydx\; =\; 0$
Divide through by [Math]y^{3}[/tex] and eventually get it into the form:
$\displaystyle 2\left( xy \right)'\; -\; \left( \frac{x^{2}}{y^{2}} \right)'\; =\; 0$
And a final family of solutions in the form of:
$\displaystyle 2xy^{3}\; -\; x^{2}\; =\; cy^{2}$