\[ 4 x^2 y''(x)+4 x^2 \log (x) y'(x)+y(x) \left (x^2 \log ^2(x)+2 x-8\right )-4 \sqrt {e^x x^{-x}} x^2=0 \] ✓ Mathematica : cpu = 0.110716 (sec), leaf count = 89
\[\left \{\left \{y(x)\to c_1 e^{x/2} x^{-\frac {x}{2}-1}+\frac {1}{3} c_2 e^{x/2} x^{2-\frac {x}{2}}-\frac {1}{9} \sqrt {e^x x^{-x}} x^2+\frac {1}{3} \sqrt {e^x x^{-x}} x^2 \log (x)\right \}\right \}\]
✓ Maple : cpu = 0.185 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{3} \left ( \ln \left ( x \right ) -{\frac {1}{3}} \right ) \sqrt {{x}^{-x}{{\rm e}^{x}}}}+{{\rm e}^{{\frac {x}{2}}}} \left ( {\it \_C1}\,{x}^{-{\frac {x}{2}}+2}+{\it \_C2}\,{x}^{-{\frac {x}{2}}-1} \right ) \right \} \]