\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a{x}^{2}-v \left ( v-1 \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.033504 (sec), leaf count = 56 \[ \left \{\left \{y(x)\to c_1 \sqrt {x} J_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right )+c_2 \sqrt {x} Y_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl J}_{v-{\frac { 1}{2}}}\left (\sqrt {a}x\right )}+{\it \_C2}\,\sqrt {x}{{\sl Y}_{v-{ \frac {1}{2}}}\left (\sqrt {a}x\right )} \right \} \]