\[ a y(x)+x^6 y^{(3)}(x)+6 x^5 y''(x)=0 \] ✓ Mathematica : cpu = 0.331787 (sec), leaf count = 102
\[\left \{\left \{y(x)\to c_1 e^{\frac {\sqrt [3]{a}}{x}} \left (2 x-\sqrt [3]{a}\right )+c_2 e^{\frac {(-1)^{2/3} \sqrt [3]{a}}{x}} \left (x-\frac {1}{2} (-1)^{2/3} \sqrt [3]{a}\right )+c_3 e^{-\frac {\sqrt [3]{-1} \sqrt [3]{a}}{x}} \left (\frac {1}{2} \sqrt [3]{-1} \sqrt [3]{a}+x\right )\right \}\right \}\] ✓ Maple : cpu = 0.543 (sec), leaf count = 291
\[y \relax (x ) = \frac {c_{1} \left (-8 x^{3}+a \right )^{4} {\mathrm e}^{-\frac {\left (-a^{4}\right )^{\frac {1}{3}}}{a x}}}{\left (2 a x +\left (-a^{4}\right )^{\frac {1}{3}}\right )^{3} \left (4 a^{2} x^{2}-2 x \left (-a^{4}\right )^{\frac {1}{3}} a +\left (-a^{4}\right )^{\frac {2}{3}}\right )^{4}}+\frac {c_{2} \left (-8 x^{3}+a \right )^{4} {\mathrm e}^{-\frac {i \left (i-\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {1}{3}}}{2 a x}}}{\left (-4 i x a +i \left (-a^{4}\right )^{\frac {1}{3}}-\left (-a^{4}\right )^{\frac {1}{3}} \sqrt {3}\right )^{3} \left (\left (-a^{4}\right )^{\frac {1}{3}} \sqrt {3}-4 i x a +i \left (-a^{4}\right )^{\frac {1}{3}}\right )^{4} \left (2 a x +\left (-a^{4}\right )^{\frac {1}{3}}\right )^{4}}+\frac {c_{3} \left (-8 x^{3}+a \right )^{4} {\mathrm e}^{-\frac {i \left (\sqrt {3}+i\right ) \left (-a^{4}\right )^{\frac {1}{3}}}{2 a x}}}{\left (\left (-a^{4}\right )^{\frac {1}{3}} \sqrt {3}-4 i x a +i \left (-a^{4}\right )^{\frac {1}{3}}\right )^{3} \left (-4 i x a +i \left (-a^{4}\right )^{\frac {1}{3}}-\left (-a^{4}\right )^{\frac {1}{3}} \sqrt {3}\right )^{4} \left (2 a x +\left (-a^{4}\right )^{\frac {1}{3}}\right )^{4}}\]