\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 4\,{x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -4\,{x}^{3}y \left ( x \right ) -4\,{x}^{5}=0} \]
Mathematica: cpu = 0.129016 (sec), leaf count = 84 \[ \left \{\left \{y(x)\to c_1 e^{-\left (1-\sqrt {2}\right ) x^2}+c_2 e^{-\left (1+\sqrt {2}\right ) x^2}-\frac {3 \sqrt {2} x^2+4 x^2+6 \sqrt {2}+8}{\sqrt {2} \left (3+2 \sqrt {2}\right )}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{2} \left ( \sqrt {2}-1 \right ) }}{\it \_C2}+{{\rm e}^{-{x}^{2} \left ( 1+\sqrt {2} \right ) }} {\it \_C1}-{x}^{2}-2 \right \} \]