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: 
http://www.wolframalpha.com/input/?i=y%27%3Dx%5E2%2By%5E2
Wikipedia has an article on this, where they give instructions on how to convert it to a second order linear differential equation. 
http://en.wikipedia.org/wiki/Riccati_equation#Reduction_to_a_second_order_linear_equation
This results in an equation 
$$u''+x^2u=0.$$
I take it this problem was not given in a typical course in differential equations? 
