\[ y''(x)=-\frac {y(x) \left (-a^2-\lambda \left (x^2-1\right )\right )}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0234926 (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 = 0.106 (sec), leaf count = 37
\[\left \{y \left (x \right ) = c_{1} \LegendreP \left (\frac {\sqrt {4 \lambda +1}}{2}-\frac {1}{2}, a , x\right )+c_{2} \LegendreQ \left (\frac {\sqrt {4 \lambda +1}}{2}-\frac {1}{2}, a , x\right )\right \}\]