\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -ay \left ( x \right ) \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) ^{3/2}=0} \]
Mathematica: cpu = 0.887113 (sec), leaf count = 350 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\frac {\text {$\#$1}^2 a+2 c_1-2}{c_1-1}} \sqrt {\frac {\text {$\#$1}^2 a+2 c_1+2}{c_1+1}} \left (F\left (i \sinh ^{-1}\left (\sqrt {\frac {a}{2 c_1+2}} \text {$\#$1}\right )|\frac {c_1+1}{c_1-1}\right )+\left (c_1-1\right ) E\left (i \sinh ^{-1}\left (\sqrt {\frac {a}{2 c_1+2}} \text {$\#$1}\right )|\frac {c_1+1}{c_1-1}\right )\right )}{\sqrt {\frac {a}{2 c_1+2}} \sqrt {\text {$\#$1}^4 a^2+4 \text {$\#$1}^2 a c_1+4 c_1^2-4}}\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {\frac {\text {$\#$1}^2 a+2 c_1-2}{c_1-1}} \sqrt {\frac {\text {$\#$1}^2 a+2 c_1+2}{c_1+1}} \left (F\left (i \sinh ^{-1}\left (\sqrt {\frac {a}{2 c_1+2}} \text {$\#$1}\right )|\frac {c_1+1}{c_1-1}\right )+\left (c_1-1\right ) E\left (i \sinh ^{-1}\left (\sqrt {\frac {a}{2 c_1+2}} \text {$\#$1}\right )|\frac {c_1+1}{c_1-1}\right )\right )}{\sqrt {\frac {a}{2 c_1+2}} \sqrt {\text {$\#$1}^4 a^2+4 \text {$\#$1}^2 a c_1+4 c_1^2-4}}\& \right ]\left [c_2+x\right ]\right \}\right \} \]
Maple: cpu = 0.140 (sec), leaf count = 106 \[ \left \{ \int ^{y \left ( x \right ) }\!{a \left ( {{\it \_a}}^{2}+2\,{ \it \_C1} \right ) {\frac {1}{\sqrt {-{{\it \_a}}^{4}{a}^{2}-4\,{\it \_C1}\,{{\it \_a}}^{2}{a}^{2}-4\,{{\it \_C1}}^{2}{a}^{2}+4}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a \left ( {{\it \_a }}^{2}+2\,{\it \_C1} \right ) {\frac {1}{\sqrt {-{{\it \_a}}^{4}{a}^{2} -4\,{\it \_C1}\,{{\it \_a}}^{2}{a}^{2}-4\,{{\it \_C1}}^{2}{a}^{2}+4}}} }{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]