Need some hints how to solve the following differential equation

$$xy'= \sqrt{y^2+x^2}+y$$

Just don't know how to begin. Thank you.
['https://math.stackexchange.com/questions/3392055', 'https://math.stackexchange.com', 'https://math.stackexchange.com/users/680628/']
Alternatively, you could try to make use of the hyperbolic identity

$$\cosh^2t - \sinh^2t = 1 \implies \cosh^2t = 1 + \sinh^2t$$

and use the inspired substitution

$$y = x\sinh\left(f(x)\right)$$

which simplifies nicely:

$$x(\sinh(f(x)) + xf'(x)\cosh(f(x))) = |x|\cosh(f(x))+x\sinh(f(x)) \implies f'(x) = \frac{1}{|x|}$$

which implies the solution is of the form

$$y = x\sinh(\text{sgn}(x)(\log(|x|)+C)) = \frac{1}{2}(Cx^2 - C^{-1})$$

So it's an upward parabola on both sides. (the $C$'s in the final answer must be positive since they are the end result of an exponentiation).
Square both sides then replace $\sqrt{y^2+x^2}$ by $xy'-y$

This becomes 

$$x^2(y')^2+y^2-xy'(1+y)-y=0$$

Now you could you appropriate subsitution