\[ b \sqrt {\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right )} y'(x)^2+y(x) \left (-2 a^2 y(x)^2+a^2+1\right ) y'(x)^2+\left (y(x)^2-1\right ) \left (a^2 y(x)^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.972327 (sec), leaf count = 124
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\exp \left (\frac {b \sqrt {1-K[1]^2} \sqrt {1-a^2 K[1]^2} F\left (\sin ^{-1}(K[1])|a^2\right )}{\sqrt {\left (K[1]^2-1\right ) \left (a^2 K[1]^2-1\right )}}+\frac {1}{2} (-\log (1-K[1])-\log (K[1]+1)-\log (1-a K[1])-\log (a K[1]+1))\right )}{c_1}dK[1]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.341 (sec), leaf count = 72
\[ \left \{ \int ^{y \left ( x \right ) }\!{{\rm e}^{\int \!{\frac {1}{ \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2}-1 \right ) } \left ( -2\,{{\it \_b}}^{3}{a}^{2}+{\it \_b}\,{a}^{2}+b\sqrt { \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2}-1 \right ) }+{\it \_b} \right ) }\,{\rm d}{\it \_b}}}{d{\it \_b}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \]