\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) \left ( {a}^{2} \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +b\sqrt { \left ( 1- \left ( y \left ( x \right ) \right ) ^{2} \right ) \left ( 1-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2} \right ) } \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( 1+{a}^{2}-2\,{a}^{2} \left ( y \left ( x \right ) \right ) ^{2} \right ) y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 103.724671 (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 = 0.110 (sec), leaf count = 72 \[ \left \{ \int ^{y \left ( x \right ) }\!{{\rm e}^{\int \!{\frac {1}{ \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2}-1 \right ) } \left ( -2\,{{\it \_b}}^{3}{a}^{2}+{\it \_b}\,{a}^{2}+b \sqrt { \left ( {{\it \_b}}^{2}-1 \right ) \left ( {{\it \_b}}^{2}{a}^{2 }-1 \right ) }+{\it \_b} \right ) }\,{\rm d}{\it \_b}}}{d{\it \_b}}-{ \it \_C1}\,x-{\it \_C2}=0 \right \} \]