\[ \left (x^2+1\right ) y'(x)+(2 x y(x)-1) \left (y(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.636967 (sec), leaf count = 203
\[\text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2} \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2}},y(x)\right ]\] ✓ Maple : cpu = 0.047 (sec), leaf count = 85
\[\left \{c_{1}+\frac {x}{\left (\left (\frac {x^{2}}{\frac {x^{4} y \left (x \right )}{x^{2}+1}-\frac {x^{3}}{x^{2}+1}}+\frac {1}{x}\right )^{2}+1\right )^{\frac {1}{4}}}+\frac {\left (x +y \left (x \right )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x +y \left (x \right )\right )^{2}}{\left (x y \left (x \right )-1\right )^{2}}\right )}{2 x y \left (x \right )-2} = 0\right \}\]