This equation is supposedly separable:

$\displaystyle t\frac{dy}{dx} = y + \sqrt{t^2 + y^2}$

but I can't separate it with algebra, and the substitutions I've tried (v=y/t, v=(t^2 + y^2)^1/2) haven't worked. The full problem, if it makes a difference, is to solve for the initial value y(1) = 0.

Could you give me a hint please?