\[ x^2 \left (-\left (y'(x)^2+1\right )\right )+2 x^2 y(x) y''(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.324443 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {x \left (c_1{}^2 \log ^2(x)-2 c_2 c_1{}^2 \log (x)+4+c_2{}^2 c_1{}^2\right )}{4 c_1}\right \}\right \}\] ✓ Maple : cpu = 0.088 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( 4\,{{\it \_C2}}^{2} \left ( \ln \left ( x \right ) \right ) ^{2}+4\,{\it \_C1}\,\ln \left ( x \right ) {\it \_C2}+{{\it \_C1}}^{2}+1 \right ) }{4\,{\it \_C2}}} \right \} \]