\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-a=0} \]
Mathematica: cpu = 0.062508 (sec), leaf count = 94 \[ \left \{\left \{y(x)\to -\frac {\sqrt {2 a^2 c_2 x+a^2 c_2^2+a^2 x^2-e^{2 c_1}}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {2 a^2 c_2 x+a^2 c_2^2+a^2 x^2-e^{2 c_1}}}{\sqrt {a}}\right \}\right \} \]
Maple: cpu = 1.669 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}},y \left ( x \right ) =-\sqrt {a{x}^{2}-2\,{\it \_C1}\,x+2\,{\it \_C2}} \right \} \]