\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac {x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}-1}}-{\frac { \left ( -{a}^{2}-\lambda \, \left ( {x}^{2}-1 \right ) \right ) y \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.021503 (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 = 0.047 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( { \frac {1}{2}\sqrt {1+4\,\lambda }}-{\frac {1}{2}},a,x \right ) +{\it \_C2}\,{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {1+4\,\lambda }}-{ \frac {1}{2}},a,x \right ) \right \} \]