\[ (1-v) v y(x)+x^2 y''(x)+2 x^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.0148909 (sec), leaf count = 62
DSolve[(1 - v)*v*y[x] + 2*x^2*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-x} \sqrt {x} J_{\frac {1}{2} (2 v-1)}(-i x)+c_2 e^{-x} \sqrt {x} Y_{\frac {1}{2} (2 v-1)}(-i x)\right \}\right \}\] ✓ Maple : cpu = 0.015 (sec), leaf count = 27
dsolve(x^2*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)-v*(v-1)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-x} \sqrt {x}\, \left (\BesselK \left (v -\frac {1}{2}, x\right ) c_{2}+\BesselI \left (v -\frac {1}{2}, x\right ) c_{1}\right )\]