\[ a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)+4 a x y^{(3)}(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.671423 (sec), leaf count = 301
\[\left \{\left \{y(x)\to \frac {2 \left (\sqrt {6}-3\right ) \sqrt {-\left (\sqrt {6}-3\right ) a} c_3 \exp \left (-\frac {a x^2}{2}-\sqrt {-\left (\sqrt {6}-3\right ) a} x-\frac {\left (-3+\sqrt {3}+\sqrt {6}\right ) a x}{\sqrt {-\left (\sqrt {6}-3\right ) a}}\right )}{\left (-3-\sqrt {3}+\sqrt {6}\right ) \left (-3+\sqrt {3}+\sqrt {6}\right ) a}+\frac {2 \left (\sqrt {6}-3\right ) \sqrt {-\left (\sqrt {6}-3\right ) a} c_4 \exp \left (-\frac {a x^2}{2}-\sqrt {-\left (\sqrt {6}-3\right ) a} x-\frac {\left (-3-\sqrt {3}+\sqrt {6}\right ) a x}{\sqrt {-\left (\sqrt {6}-3\right ) a}}\right )}{\left (-3-\sqrt {3}+\sqrt {6}\right ) \left (-3+\sqrt {3}+\sqrt {6}\right ) a}+c_1 e^{-\frac {a x^2}{2}-\sqrt {-\left (\sqrt {6}-3\right ) a} x}+c_2 e^{\sqrt {-\left (\sqrt {6}-3\right ) a} x-\frac {a x^2}{2}}\right \}\right \}\]
✓ Maple : cpu = 0.052 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {a{x}^{2}}{2}}}} \left ( {\it \_C1}\,{{\rm e}^{-\sqrt {-a\sqrt {6}+3\,a}x}}+{\it \_C2}\,{{\rm e}^{\sqrt {-a\sqrt {6}+3\,a}x}}+{\it \_C3}\,{{\rm e}^{-\sqrt {a\sqrt {6}+3\,a}x}}+{\it \_C4}\,{{\rm e}^{\sqrt {a\sqrt {6}+3\,a}x}} \right ) \right \} \]