\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,{x}^{3}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\,{x}^{4}+2\,{x}^{2}+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.055007 (sec), leaf count = 68 \[ \left \{\left \{y(x)\to c_1 e^{-x^2} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}}-\frac {i c_2 e^{-x^2} x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}}}{\sqrt {3}}\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {1}{2}}+{\frac {i }{2}}\sqrt {3}}{{\rm e}^{-{x}^{2}}}+{\it \_C2}\,{x}^{{\frac {1}{2}}-{ \frac {i}{2}}\sqrt {3}}{{\rm e}^{-{x}^{2}}} \right \} \]