\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) a{x}^{3}=0} \]
Mathematica: cpu = 0.008501 (sec), leaf count = 41 \[ \left \{\left \{y(x)\to c_1 \cosh \left (\frac {\sqrt {a} x^2}{2}\right )+i c_2 \sinh \left (\frac {\sqrt {a} x^2}{2}\right )\right \}\right \} \]
Maple: cpu = 0.0 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sinh \left ( {\frac {{x}^{2} }{2}\sqrt {a}} \right ) +{\it \_C2}\,\cosh \left ( {\frac {{x}^{2}}{2} \sqrt {a}} \right ) \right \} \]