2.339   ODE No. 339

\[ \left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)-\sqrt {x^2+y(x)^2+1} y(x)-x \left (x^2+y(x)^2\right )=0 \] Mathematica : cpu = 0.354526 (sec), leaf count = 27


\[\text {Solve}\left [\sqrt {x^2+y(x)^2+1}+\tan ^{-1}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ]\] Maple : cpu = 0.204 (sec), leaf count = 27


\[\arctan \left (\frac {y \relax (x )}{x}\right )-\sqrt {x^{2}+y \relax (x )^{2}+1}-c_{1} = 0\]