2.1371   ODE No. 1371

\[ y''(x)=-\frac {y(x) \left (-a^2-\lambda \left (x^2-1\right )\right )}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] Mathematica : cpu = 0.0149352 (sec), leaf count = 48


\[\left \{\left \{y(x)\to c_1 P_{\frac {1}{2} \left (\sqrt {4 \lambda +1}-1\right )}^a(x)+c_2 Q_{\frac {1}{2} \left (\sqrt {4 \lambda +1}-1\right )}^a(x)\right \}\right \}\] Maple : cpu = 0.053 (sec), leaf count = 37


\[y \relax (x ) = c_{1} \LegendreP \left (\frac {\sqrt {1+4 \lambda }}{2}-\frac {1}{2}, a , x\right )+c_{2} \LegendreQ \left (\frac {\sqrt {1+4 \lambda }}{2}-\frac {1}{2}, a , x\right )\]