# Calculation of differential equation $\large \frac{dy}{dx} = \frac{1}{x^2+y^2}$

Calculation of differential equation $\displaystyle \frac{dy}{dx} = \frac{1}{x^2+y^2}$

I have tried like this way put $y=vx$ and $\displaystyle \frac{dy}{dx} = v+x.\frac{dv}{dx}$

so $\displaystyle v+ x.\frac{dv}{dx} = \frac{1}{x^2.(1+v^2)}$

Now after that how can i proceed

Thanks

-

Without loss of generality, we can switch $x$ and $y$, and write $$y'=x^2+y^2.$$ Plugging this into wolfram alpha, we see this is an example of the Riccatis' equations:
This results in an equation $$u''+x^2u=0.$$ I take it this problem was not given in a typical course in differential equations?
$x'$ not $y'$ in the second line. ;-) –  B. S. Mar 24 '13 at 2:13