\[ ((2 v+5) x-2 v-3) y'(x)+(v+1) y(x)+2 (x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.0491746 (sec), leaf count = 60
DSolve[(1 + v)*y[x] + (-3 - 2*v + (5 + 2*v)*x)*Derivative[1][y][x] + 2*(-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 i^{-2 v-1} x^{\frac {1}{2} (-2 v-1)} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},-v,\frac {1}{2}-v,x\right )+c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{2},v+1,v+\frac {3}{2},x\right )\right \}\right \}\] ✓ Maple : cpu = 0.145 (sec), leaf count = 40
dsolve(2*x*(x-1)*diff(diff(y(x),x),x)+((2*v+5)*x-2*v-3)*diff(y(x),x)+(v+1)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}+v \right ], x\right )+c_{2} x^{-\frac {1}{2}-v} \operatorname {hypergeom}\left (\left [\frac {1}{2}, -v \right ], \left [\frac {1}{2}-v \right ], x\right )\]