\[ a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)+4 a x y^{(3)}(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.741548 (sec), leaf count = 139
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x \left (a x+2 \sqrt {-\left (\sqrt {6}-3\right ) a}\right )} \left (c_2 e^{2 \sqrt {-\left (\sqrt {6}-3\right ) a} x}+\frac {\sqrt {\frac {1}{2}-\frac {1}{\sqrt {6}}} e^{-\frac {\left (-3+\sqrt {3}+\sqrt {6}\right ) a x}{\sqrt {-\left (\sqrt {6}-3\right ) a}}} \left (c_4 e^{\frac {2 a x}{\sqrt {a-\sqrt {\frac {2}{3}} a}}}+c_3\right )}{\sqrt {a}}+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.059 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {a{x}^{2}}{2}}}} \left ( {\it \_C2}\,{{\rm e}^{\sqrt {-a \left ( \sqrt {6}-3 \right ) }x}}+{\it \_C4}\,{{\rm e}^{\sqrt { \left ( 3+\sqrt {6} \right ) a}x}}+{\it \_C1}\,{{\rm e}^{-\sqrt {-a \left ( \sqrt {6}-3 \right ) }x}}+{\it \_C3}\,{{\rm e}^{-\sqrt { \left ( 3+\sqrt {6} \right ) a}x}} \right ) \right \} \]