\[ a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0 \] ✓ Mathematica : cpu = 10.5829 (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 = 0.991 (sec), leaf count = 94
\[\int _{}^{y \relax (x )}\frac {a \left (\textit {\_a}^{2}+2 c_{1}\right )}{\sqrt {-\left (-1+a \left (\textit {\_a}^{2}+2 c_{1}\right )\right ) a \left (\textit {\_a}^{2}+2 c_{1}\right )}}d \textit {\_a} -x -c_{2} = 0\]