\[ y(x) \left (a x^2+(1-v) v\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0285052 (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 = 0.036 (sec), leaf count = 31
\[\left \{y \left (x \right ) = \left (c_{1} \BesselJ \left (v -\frac {1}{2}, \sqrt {a}\, x \right )+c_{2} \BesselY \left (v -\frac {1}{2}, \sqrt {a}\, x \right )\right ) \sqrt {x}\right \}\]