\[ \left (x^2+1\right ) y'(x)+(2 x y(x)-1) \left (y(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.409314 (sec), leaf count = 203
DSolve[(-1 + 2*x*y[x])*(1 + y[x]^2) + (1 + x^2)*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2}},y(x)\right ]\] ✓ Maple : cpu = 0.036 (sec), leaf count = 76
dsolve((x^2+1)*diff(y(x),x)+(y(x)^2+1)*(2*x*y(x)-1) = 0,y(x))
\[c_{1}+\frac {x}{{\left (1+\left (\frac {1}{x}+\frac {x^{2} \left (x^{2}+1\right )}{y \left (x \right ) x^{4}-x^{3}}\right )^{2}\right )}^{\frac {1}{4}}}+\frac {\left (y \left (x \right )+x \right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (y \left (x \right )+x \right )^{2}}{\left (x y \left (x \right )-1\right )^{2}}\right )}{2 x y \left (x \right )-2} = 0\]