\[ a \left (y'(x)^2+1\right )+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.525633 (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 = 1.245 (sec), leaf count = 68
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{-a}}{\frac {1}{\sqrt {-{{\it \_a}}^{2\,a}+{\it \_C1}}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{{{\it \_a}}^{-a}}{\frac {1}{\sqrt {-{{\it \_a}}^{2\,a}+{\it \_C1}}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]