\[ a y(x)+v y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0265865 (sec), leaf count = 104
DSolve[a*y[x] + v*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 a^{\frac {v-1}{2}-v+1} x^{\frac {v-1}{2}-v+1} \Gamma (2-v) J_{1-v}\left (2 \sqrt {a} \sqrt {x}\right )+c_1 a^{\frac {1-v}{2}} x^{\frac {1-v}{2}} \Gamma (v) J_{v-1}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.014 (sec), leaf count = 41
dsolve(x*diff(diff(y(x),x),x)+v*diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = x^{\frac {1}{2}-\frac {v}{2}} \left (\BesselY \left (v -1, 2 \sqrt {a}\, \sqrt {x}\right ) c_{2}+\BesselJ \left (v -1, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1}\right )\]