\[ 4 x^2 y''(x)+4 x^2 \log (x) y'(x)+y(x) \left (x^2 \log ^2(x)+2 x-8\right )-4 \sqrt {e^x x^{-x}} x^2=0 \] ✓ Mathematica : cpu = 0.060708 (sec), leaf count = 90
\[\left \{\left \{y(x)\to c_1 e^{x/2} x^{-\frac {x}{2}-1}+\frac {1}{3} c_2 e^{x/2} x^{2-\frac {x}{2}}+\frac {1}{9} \left (3 x^2 \sqrt {e^x x^{-x}} \log (x)-x^2 \sqrt {e^x x^{-x}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.119 (sec), leaf count = 48
\[y \relax (x ) = \frac {\left (\ln \relax (x )-\frac {1}{3}\right ) x^{2} \sqrt {x^{-x} {\mathrm e}^{x}}}{3}+{\mathrm e}^{\frac {x}{2}} \left (c_{1} x^{-\frac {x}{2}+2}+c_{2} x^{-\frac {x}{2}-1}\right )\]