\[ \boxed { 4\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,{x}^{2}\ln \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {x}^{2} \left ( \ln \left ( x \right ) \right ) ^{2}+2\,x-8 \right ) y \left ( x \right ) -4\,{x}^{2}\sqrt {{\frac {{{\rm e}^{x}}}{{x}^{x}}}}=0} \]
Mathematica: cpu = 0.098513 (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 = 0.093 (sec), leaf count = 52 \[ \left \{ y \left ( x \right ) ={x}^{-{\frac {x}{2}}-1}{{\rm e}^{{\frac { x}{2}}}}{\it \_C2}+{x}^{-{\frac {x}{2}}+2}{{\rm e}^{{\frac {x}{2}}}}{ \it \_C1}+{\frac {{x}^{2} \left ( 3\,\ln \left ( x \right ) -1 \right ) }{9}\sqrt {{x}^{-x}{{\rm e}^{x}}}} \right \} \]