ODE No. 1256

$$-v(v+1)y(x)+(x-1)x{y}^{″}(x)+(2x-1)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0172269 (sec), leaf count = 26

DSolve[-(v*(1 + v)*y[x]) + (-1 + 2*x)*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

$$\{\{y(x)\to c_1{P}_v(2x-1)+c_2{Q}_v(2x-1)\}\}$$ ✓ Maple : cpu = 0.085 (sec), leaf count = 51

dsolve(x*(x-1)*diff(diff(y(x),x),x)+(2*x-1)*diff(y(x),x)-v*(v+1)*y(x)=0,y(x))
 

$$y\left(x\right)=c_1\mathrm{hypergeom}([-v,-v],[-2v],\frac{1}{x})x^v+c_2\mathrm{hypergeom}([v+1,v+1],[2v+2],\frac{1}{x})x^{-v-1}$$