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 = 0.393367 (sec), leaf count = 27

DSolve[-(x*(x^2 + y[x]^2)) - y[x]*Sqrt[1 + x^2 + y[x]^2] + (-(y[x]*(x^2 + y[x]^2)) + x*Sqrt[1 + x^2 + y[x]^2])*Derivative[1][y][x] == 0,y[x],x]

\[\text {Solve}\left [\sqrt {x^2+y(x)^2+1}+\tan ^{-1}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.2 (sec), leaf count = 25

dsolve((x*(x^2+y(x)^2+1)^(1/2)-y(x)*(y(x)^2+x^2))*diff(y(x),x)-y(x)*(x^2+y(x)^2+1)^(1/2)-x*(y(x)^2+x^2) = 0,y(x))

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