\[ a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0 \] ✓ Mathematica : cpu = 10.6045 (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 = 0.433 (sec), leaf count = 94
\[ \left \{ \int ^{y \left ( x \right ) }\!{a \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) {\frac {1}{\sqrt {-a \left ( -1+a \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) \right ) \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) {\frac {1}{\sqrt {-a \left ( -1+a \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) \right ) \left ( {{\it \_a}}^{2}+2\,{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]