\[ y''(x)^2 \left (a^2 y(x)^2-b^2\right )+y'(x)^2 \left (a^2 y'(x)^2-1\right )-2 a^2 y(x) y'(x)^2 y''(x)=0 \] ✗ Mathematica : cpu = 3600.91 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 3.947 (sec), leaf count = 162
\[ \left \{ y \left ( x \right ) ={\it \_C1},y \left ( x \right ) ={\frac {b}{a}},y \left ( x \right ) ={b \left ( {{\rm e}^{{\frac {{\it \_C2}+x}{b}\sqrt {{{\it \_C1}}^{2}{a}^{2}-1}}}}-{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_C1}}^{2}{a}^{2}-1}}}},y \left ( x \right ) ={\frac {b}{a}\tan \left ( {\frac {{\it \_C1}-x}{ab}\sqrt {{a}^{2}}} \right ) {\frac {1}{\sqrt { \left ( \tan \left ( {\frac {{\it \_C1}-x}{ab}\sqrt {{a}^{2}}} \right ) \right ) ^{2}+1}}}},y \left ( x \right ) =-{\frac {b}{a}},y \left ( x \right ) =-{\frac {b}{a}\tan \left ( {\frac {{\it \_C1}-x}{ab}\sqrt {{a}^{2}}} \right ) {\frac {1}{\sqrt { \left ( \tan \left ( {\frac {{\it \_C1}-x}{ab}\sqrt {{a}^{2}}} \right ) \right ) ^{2}+1}}}} \right \} \]