\[ 2 \left (x^2+1\right ) y''(x)^2-x \left (4 y'(x)+x\right ) y''(x)+2 y'(x) \left (y'(x)+x\right )-2 y(x)=0 \] ✓ Mathematica : cpu = 0.0073533 (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 = 1.424 (sec), leaf count = 59
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{{\it \_C1}}^{2}+{{\it \_C2}}^{2},y \left ( x \right ) ={\frac {x}{2} \left ( {\it \_C1}+{\frac {{\it Arcsinh} \left ( x \right ) }{4}} \right ) \sqrt {{x}^{2}+1}}-{\frac {3\,{x}^{2}}{16}}+{{\it \_C1}}^{2}+{\frac {{\it \_C1}\,{\it Arcsinh} \left ( x \right ) }{2}}+{\frac { \left ( {\it Arcsinh} \left ( x \right ) \right ) ^{2}}{16}} \right \} \]