ODE No. 1361

\[ y''(x)=\frac {2 x y'(x)}{x^2-1}-\frac {\left (a (a+1)-a (a+3) x^2\right ) y(x)}{x^2 \left (x^2-1\right )} \]

✓ Mathematica : cpu = 0.259099 (sec), leaf count = 38

DSolve[Derivative[2][y][x] == -(((a*(1 + a) - a*(3 + a)*x^2)*y[x])/(x^2*(-1 + x^2))) + (2*x*Derivative[1][y][x])/(-1 + x^2),y[x],x]

\[\left \{\left \{y(x)\to c_1 x^{-a}+c_2 \left (-2 a x^2+2 a-x^2+3\right ) x^{a+1}\right \}\right \}\]

✓ Maple : cpu = 0.047 (sec), leaf count = 33

dsolve(diff(diff(y(x),x),x) = 2*x/(x^2-1)*diff(y(x),x)-(a*(a+1)-a*x^2*(a+3))/x^2/(x^2-1)*y(x),y(x))

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