TITLE: Differential Equation$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{x^{2}+y^{2}}$
QUESTION [5 upvotes]: Please give me a hint to solve for $y$. Given,
$$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{x^{2}+y^{2}}$$  
I took $y=x\cdot\tan\theta$ but it was of no use.

REPLY [2 votes]: I would guess that it's not solvable in closed form. By taking "the reciprocal" of both sides,
$$\frac{\mathrm{d}x}{\mathrm{d}y} = x^2 + y^2$$
I couldn't find a solution to this form either, and if you put it into Wolfram Alpha you get a really horrible looking answer for which I can't imagine a possible method.
Maybe someone who knows some advanced techniques will be able to help you more.