\[ b \sqrt {\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right )} y'(x)^2+\left (y(x)^2-1\right ) \left (a^2 y(x)^2-1\right ) y''(x)+y(x) \left (-2 a^2 y(x)^2+a^2+1\right ) y'(x)^2=0 \] ✓ Mathematica : cpu = 104.637 (sec), leaf count = 172
\[\text {Solve}\left [\log (x)-b \left (\frac {\log \left (b c_1 \sqrt {1-y(x)^2} \sqrt {1-a^2 y(x)^2}+\sqrt {y(x)^2-1} \sqrt {a^2 y(x)^2-1} \exp \left (\frac {b \sqrt {1-y(x)^2} \sqrt {1-a^2 y(x)^2} F\left (\sin ^{-1}(y(x))|a^2\right )}{\sqrt {y(x)^2-1} \sqrt {a^2 y(x)^2-1}}\right )\right )}{b}-\frac {\log \left (1-a^2 y(x)^2\right )}{2 b}-\frac {\log \left (1-y(x)^2\right )}{2 b}\right )=c_2,y(x)\right ]\] ✓ Maple : cpu = 0.163 (sec), leaf count = 72
\[ \left \{ \int ^{y \left ( x \right ) }\!{{\rm e}^{\int \!{\frac {1}{ \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2}-1 \right ) } \left ( -2\,{{\it \_b}}^{3}{a}^{2}+{\it \_b}\,{a}^{2}+b\sqrt { \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2}-1 \right ) }+{\it \_b} \right ) }\,{\rm d}{\it \_b}}}{d{\it \_b}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \]