\[ y(x) \left (a x^2-(v-1) v\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0347533 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \sqrt {x} \left (c_1 J_{v-\frac {1}{2}}\left (\sqrt {a} x\right )+c_2 Y_{v-\frac {1}{2}}\left (\sqrt {a} x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.029 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )}{\it \_C2}+{{\sl J}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )}{\it \_C1} \right ) \right \} \]