2.1247   ODE No. 1247

\[ 2 a x y'(x)+(a-1) a y(x)+\left (x^2-1\right ) y''(x)=0 \] Mathematica : cpu = 0.156767 (sec), leaf count = 128


\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {1-x^2} (x+1)^{\sqrt {(a-1)^2}} \left (x^2-1\right )^{-a/2} (1-x)^{-\sqrt {(a-1)^2}} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)}}{2 \sqrt {(a-1)^2}}+c_1 \sqrt {1-x^2} \left (x^2-1\right )^{-a/2} e^{-\sqrt {(a-1)^2} \tanh ^{-1}(x)}\right \}\right \}\] Maple : cpu = 0.035 (sec), leaf count = 27


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