# separable or non-separable ODE

#### wmccunes

##### New member
I haven't done ODEs in a while nor have a book handing.

How do I tackle an equation of the form
$2xyy'=-x^2-y^2$
I tried polar but that didn't seem to work.

#### chisigma

##### Well-known member
Re: separable or not separable ODE

I haven't done ODEs in a while nor have a book handing.

How do I tackle an equation of the form
$2xyy'=-x^2-y^2$
I tried polar but that didn't seem to work.
With simple steps Yoy arrive to write...

$\displaystyle (x^{2} + y^{2})\ dx + 2\ x\ y\ d y =0\ (1)$

... and the expression (1) is an 'exact differential'...

Kind regards

$\chi$ $\sigma$

#### MarkFL

$$\displaystyle \frac{dy}{dx}=-\frac{1}{2}\left(\frac{x}{y}+\frac{y}{x} \right)$$
$$\displaystyle v=\frac{y}{x}$$