\[ 2 x^2 y(x) y''(x)-\left (x^2 \left (y'(x)^2+1\right )\right )+y(x)^2=0 \] ✓ Mathematica : cpu = 0.377853 (sec), leaf count = 44
DSolve[y[x]^2 - x^2*(1 + Derivative[1][y][x]^2) + 2*x^2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {x \left (c_1{}^2 \log ^2(x)-2 c_2 c_1{}^2 \log (x)+4+c_2{}^2 c_1{}^2\right )}{4 c_1}\right \}\right \}\] ✓ Maple : cpu = 0.916 (sec), leaf count = 30
dsolve(2*x^2*y(x)*diff(diff(y(x),x),x)-x^2*(diff(y(x),x)^2+1)+y(x)^2=0,y(x))
\[y \left (x \right ) = \frac {x \left (4 c_{2}^{2} \ln \left (x \right )^{2}+4 c_{1} \ln \left (x \right ) c_{2}+c_{1}^{2}+1\right )}{4 c_{2}}\]