\[ a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0 \] ✓ Mathematica : cpu = 10.8422 (sec), leaf count = 262
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\frac {\text {$\#$1}^2 (-a)+1+2 c_1}{1+2 c_1}} \sqrt {2 \text {$\#$1}^2 a-4 c_1} E\left (\sin ^{-1}\left (\sqrt {\frac {a}{2 c_1+1}} \text {$\#$1}\right )|1+\frac {1}{2 c_1}\right )}{\sqrt {\frac {a}{1+2 c_1}} \sqrt {\text {$\#$1}^2 (-a)+1+2 c_1} \sqrt {2-\frac {\text {$\#$1}^2 a}{c_1}}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {\frac {\text {$\#$1}^2 (-a)+1+2 c_1}{1+2 c_1}} \sqrt {2 \text {$\#$1}^2 a-4 c_1} E\left (\sin ^{-1}\left (\sqrt {\frac {a}{2 c_1+1}} \text {$\#$1}\right )|1+\frac {1}{2 c_1}\right )}{\sqrt {\frac {a}{1+2 c_1}} \sqrt {\text {$\#$1}^2 (-a)+1+2 c_1} \sqrt {2-\frac {\text {$\#$1}^2 a}{c_1}}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.322 (sec), leaf count = 94
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {\left (\textit {\_a}^{2}+2 c_{1}\right ) a}{\sqrt {-\left (\left (\textit {\_a}^{2}+2 c_{1}\right ) a -1\right ) \left (\textit {\_a}^{2}+2 c_{1}\right ) a}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}-\frac {\left (\textit {\_a}^{2}+2 c_{1}\right ) a}{\sqrt {-\left (\left (\textit {\_a}^{2}+2 c_{1}\right ) a -1\right ) \left (\textit {\_a}^{2}+2 c_{1}\right ) a}}d \textit {\_a} = 0\right \}\]