\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +v{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.035505 (sec), leaf count = 104 \[ \left \{\left \{y(x)\to c_2 a^{\frac {v-1}{2}-v+1} x^{\frac {v-1}{2}-v+1} \Gamma (2-v) J_{1-v}\left (2 \sqrt {a} \sqrt {x}\right )+c_1 a^{\frac {1-v}{2}} x^{\frac {1-v}{2}} \Gamma (v) J_{v-1}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {1}{2}}-{\frac {v }{2}}}{{\sl J}_{v-1}\left (2\,\sqrt {a}\sqrt {x}\right )}+{\it \_C2}\,{x }^{{\frac {1}{2}}-{\frac {v}{2}}}{{\sl Y}_{v-1}\left (2\,\sqrt {a} \sqrt {x}\right )} \right \} \]