\[ a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)+4 a x y^{(3)}(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.459712 (sec), leaf count = 300
DSolve[a^4*x^4*y[x] + 4*a^3*x^3*Derivative[1][y][x] + 6*a^2*x^2*Derivative[2][y][x] + 4*a*x*Derivative[3][y][x] + Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {2 \left (\sqrt {6}-3\right ) \sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} c_3 \exp \left (-\frac {a x^2}{2}-\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} x-\frac {\left (-3+\sqrt {3}+\sqrt {6}\right ) a x}{\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )}}\right )}{\left (-3-\sqrt {3}+\sqrt {6}\right ) \left (-3+\sqrt {3}+\sqrt {6}\right ) a}-\frac {2 \left (\sqrt {6}-3\right ) \sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} c_4 \exp \left (-\frac {a x^2}{2}-\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} x+\frac {\left (3+\sqrt {3}-\sqrt {6}\right ) a x}{\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )}}\right )}{\left (3+\sqrt {3}-\sqrt {6}\right ) \left (-3+\sqrt {3}+\sqrt {6}\right ) a}+c_1 e^{-\frac {a x^2}{2}-\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} x}+c_2 e^{\sqrt {-\left (\left (\sqrt {6}-3\right ) a\right )} x-\frac {a x^2}{2}}\right \}\right \}\] ✓ Maple : cpu = 0.053 (sec), leaf count = 73
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+4*a*x*diff(diff(diff(y(x),x),x),x)+6*a^2*x^2*diff(diff(y(x),x),x)+4*a^3*x^3*diff(y(x),x)+a^4*x^4*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {a \,x^{2}}{2}} \left (c_{2} {\mathrm e}^{\sqrt {-a \left (\sqrt {6}-3\right )}\, x}+c_{4} {\mathrm e}^{\sqrt {\left (3+\sqrt {6}\right ) a}\, x}+c_{1} {\mathrm e}^{-\sqrt {-a \left (\sqrt {6}-3\right )}\, x}+c_{3} {\mathrm e}^{-\sqrt {\left (3+\sqrt {6}\right ) a}\, x}\right )\]