2.1359   ODE No. 1359

\[ y''(x)=-\frac {v (v+1) y(x)}{x^2 \left (x^2-1\right )}-\frac {2 x y'(x)}{x^2-1} \]

✓ Mathematica : cpu = 0.0531723 (sec), leaf count = 86

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

\[\left \{\left \{y(x)\to c_1 i^{-v} x^{-v} \, _2F_1\left (\frac {1}{2}-\frac {v}{2},-\frac {v}{2};\frac {1}{2}-v;x^2\right )+c_2 i^{v+1} x^{v+1} \, _2F_1\left (\frac {v}{2}+\frac {1}{2},\frac {v}{2}+1;v+\frac {3}{2};x^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.147 (sec), leaf count = 57

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

\[y \left (x \right ) = c_{1} x^{-v} \operatorname {hypergeom}\left (\left [-\frac {v}{2}, \frac {1}{2}-\frac {v}{2}\right ], \left [\frac {1}{2}-v \right ], x^{2}\right )+c_{2} x^{v +1} \operatorname {hypergeom}\left (\left [1+\frac {v}{2}, \frac {1}{2}+\frac {v}{2}\right ], \left [\frac {3}{2}+v \right ], x^{2}\right )\]