\[ 4 x^2 y''(x)+4 x^2 \log (x) y'(x)+y(x) \left (x^2 \log ^2(x)+2 x-8\right )-4 \sqrt {e^x x^{-x}} x^2=0 \] ✓ Mathematica : cpu = 0.104897 (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 = 0.136 (sec), leaf count = 52
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {x}{2}}-1}{{\rm e}^{{\frac {x}{2}}}}{\it \_C2}+{x}^{-{\frac {x}{2}}+2}{{\rm e}^{{\frac {x}{2}}}}{\it \_C1}+{\frac {{x}^{2} \left ( 3\,\ln \left ( x \right ) -1 \right ) }{9}\sqrt {{x}^{-x}{{\rm e}^{x}}}} \right \} \]