\[ a \left (y'(x)^2+1\right )+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.529864 (sec), leaf count = 172
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\text {$\#$1} \sqrt {1-e^{2 c_1} \text {$\#$1}^{-2 a}} \, _2F_1\left (\frac {1}{2},-\frac {1}{2 a};1-\frac {1}{2 a};e^{2 c_1} \text {$\#$1}^{-2 a}\right )}{\sqrt {-1+e^{2 c_1} \text {$\#$1}^{-2 a}}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \sqrt {1-e^{2 c_1} \text {$\#$1}^{-2 a}} \, _2F_1\left (\frac {1}{2},-\frac {1}{2 a};1-\frac {1}{2 a};e^{2 c_1} \text {$\#$1}^{-2 a}\right )}{\sqrt {-1+e^{2 c_1} \text {$\#$1}^{-2 a}}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.119 (sec), leaf count = 68
\[\int _{}^{y \relax (x )}\frac {\textit {\_a}^{a}}{\sqrt {-\textit {\_a}^{2 a}+c_{1}}}d \textit {\_a} -x -c_{2} = 0\]