Question: How would I solve this differential eqn

$$xdy - ydx = (x^2 + y^2)^{1/2} dx$$

I tried bringing the sq root term to the left and it looked like a trigonometric substitution might do the trick, but apparently no.

Any help would be appreciated.

Answer: 
$$x\frac{dy}{dx} - y = (x^2 + y^2)^{1/2} $$ is an ODE of the homogeneous kind. The usual method to solve it is to let $y(x)=x\:f(x)$

This leads to an ODE of the separable kind easy to solve.

The final result is $y=c\:x^2-\frac{1}{4\:c}$
The substitution $y = u x$ makes this into a separable differential equation.