\[ a y(x)+v y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0375991 (sec), leaf count = 77
\[\left \{\left \{y(x)\to a^{\frac {1}{2}-\frac {v}{2}} x^{\frac {1}{2}-\frac {v}{2}} \left (c_2 \Gamma (2-v) J_{1-v}\left (2 \sqrt {a} \sqrt {x}\right )+c_1 \Gamma (v) J_{v-1}\left (2 \sqrt {a} \sqrt {x}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.015 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={x}^{{\frac {1}{2}}-{\frac {v}{2}}} \left ( {{\sl Y}_{v-1}\left (2\,\sqrt {a}\sqrt {x}\right )}{\it \_C2}+{{\sl J}_{v-1}\left (2\,\sqrt {a}\sqrt {x}\right )}{\it \_C1} \right ) \right \} \]