\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) ^{3/2}=0} \]
Mathematica: cpu = 0.071509 (sec), leaf count = 75 \[ \left \{\left \{y(x)\to c_2-\frac {i \sqrt {a^2 x^2+2 a c_1 x+c_1^2-1}}{a}\right \},\left \{y(x)\to c_2+\frac {i \sqrt {a^2 x^2+2 a c_1 x+c_1^2-1}}{a}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\,a+ax-1 \right ) \left ( {\it \_C1}\,a+ax+1 \right ) }{a}\sqrt {- \left ( {{\it \_C1}}^{2}{a}^{2}+2\,{\it \_C1}\,{a}^{2}x+{a}^{2}{x}^{2}-1 \right ) ^{- 1}}}+{\it \_C2} \right \} \]