\[ y''(x)^2 \left (a^2 y(x)^2-b^2\right )+y'(x)^2 \left (a^2 y'(x)^2-1\right )-2 a^2 y(x) y'(x)^2 y''(x)=0 \] ✓ Mathematica : cpu = 121.475 (sec), leaf count = 81
\[\left \{\left \{y(x)\to \frac {b \left (e^{\frac {\sqrt {-1+a^2 c_1{}^2} (x+c_2)}{b}}-c_1\right )}{\sqrt {-1+a^2 c_1{}^2}}\right \},\left \{y(x)\to c_1 e^{c_2 x}-\frac {\sqrt {b^2+\frac {1}{c_2{}^2}}}{a}\right \}\right \}\] ✓ Maple : cpu = 6.829 (sec), leaf count = 162
\[\left \{y \left (x \right ) = c_{1}, y \left (x \right ) = \frac {b}{a}, y \left (x \right ) = \frac {\left (-c_{1}+{\mathrm e}^{\frac {\sqrt {c_{1}^{2} a^{2}-1}\, \left (c_{2}+x \right )}{b}}\right ) b}{\sqrt {c_{1}^{2} a^{2}-1}}, y \left (x \right ) = \frac {b \tan \left (\frac {\sqrt {a^{2}}\, \left (c_{1}-x \right )}{a b}\right )}{\sqrt {\tan ^{2}\left (\frac {\sqrt {a^{2}}\, \left (c_{1}-x \right )}{a b}\right )+1}\, a}, y \left (x \right ) = -\frac {b}{a}, y \left (x \right ) = -\frac {b \tan \left (\frac {\sqrt {a^{2}}\, \left (c_{1}-x \right )}{a b}\right )}{\sqrt {\tan ^{2}\left (\frac {\sqrt {a^{2}}\, \left (c_{1}-x \right )}{a b}\right )+1}\, a}\right \}\]