2.1256   ODE No. 1256

\[ -v (v+1) y(x)+(x-1) x y''(x)+(2 x-1) y'(x)=0 \]

✓ Mathematica : cpu = 0.0119486 (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]
 

\[\{\{y(x)\to c_1 P_v(2 x-1)+c_2 Q_v(2 x-1)\}\}\]

✓ Maple : cpu = 0.155 (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))
 

\[y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [-v , -v \right ], \left [-2 v \right ], \frac {1}{x}\right ) x^{v}+c_{2} \operatorname {hypergeom}\left (\left [v +1, v +1\right ], \left [2 v +2\right ], \frac {1}{x}\right ) x^{-v -1}\]