\[ \left (x^2+y(x)^2\right ) y''(x)+\left (y(x)-x y'(x)\right ) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.294842 (sec), leaf count = 74
DSolve[(y[x] - x*Derivative[1][y][x])*(1 + Derivative[1][y][x]^2) + (x^2 + y[x]^2)*Derivative[2][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {1}{2} \left (\log \left (1-\frac {i y(x)}{x}\right )+\log \left (1+\frac {i y(x)}{x}\right )+i \cot (c_1) \left (\log \left (1-\frac {i y(x)}{x}\right )-\log \left (1+\frac {i y(x)}{x}\right )\right )\right )=-\log (x)+c_2,y(x)\right ]\] ✓ Maple : cpu = 1.488 (sec), leaf count = 82
dsolve((y(x)^2+x^2)*diff(diff(y(x),x),x)-(diff(y(x),x)^2+1)*(x*diff(y(x),x)-y(x))=0,y(x))
\[y \left (x \right ) = \tan \left (\RootOf \left (-{\mathrm e}^{\frac {2 i c_{1} \textit {\_Z}}{-1+c_{1}}} {\mathrm e}^{\frac {2 c_{1} c_{2}}{-1+c_{1}}} x^{\frac {2 c_{1}}{-1+c_{1}}} {\mathrm e}^{\frac {2 i \textit {\_Z}}{-1+c_{1}}}+\left (\cos ^{2}\left (\textit {\_Z} \right )\right ) {\mathrm e}^{\frac {2 c_{2}}{-1+c_{1}}} x^{\frac {2}{-1+c_{1}}}\right )\right ) x\]