\[ y''(x)=-\frac {y(x) \left (-a^2-\lambda \left (x^2-1\right )\right )}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.021603 (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 = 0.065 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( {\frac {1}{2}\sqrt {1+4\,\lambda }}-{\frac {1}{2}},a,x \right ) +{\it \_C2}\,{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {1+4\,\lambda }}-{\frac {1}{2}},a,x \right ) \right \} \]