\[ 2 \left (x^2+1\right ) y''(x)^2+2 y'(x) \left (y'(x)+x\right )-x \left (4 y'(x)+x\right ) y''(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.0101352 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {c_2-c_1^2} x^2+c_1 x+c_2\right \}\right \}\]
✓ Maple : cpu = 0.95 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{{\it \_C1}}^{2}+{{\it \_C2}}^{2},y \left ( x \right ) =-{\frac {3\,{x}^{2}}{16}}+{\frac {{\it Arcsinh} \left ( x \right ) x}{8}\sqrt {{x}^{2}+1}}+{\frac { \left ( {\it Arcsinh} \left ( x \right ) \right ) ^{2}}{16}}+{\it \_C1}\, \left ( {\frac {x}{2}\sqrt {{x}^{2}+1}}+{\frac {{\it Arcsinh} \left ( x \right ) }{2}} \right ) +{{\it \_C1}}^{2} \right \} \]