\[ \boxed { \left ( y \left ( x \right ) \right ) ^{3}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a=0} \]
Mathematica: cpu = 1.945247 (sec), leaf count = 88 \[ \left \{\left \{y(x)\to -\frac {\sqrt {a+c_1^2 x^2+2 c_2 c_1^2 x+c_2^2 c_1^2}}{\sqrt {c_1}}\right \},\left \{y(x)\to \frac {\sqrt {a+c_1^2 x^2+2 c_2 c_1^2 x+c_2^2 c_1^2}}{\sqrt {c_1}}\right \}\right \} \]
Maple: cpu = 1.762 (sec), leaf count = 70 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\, \left ( {{\it \_C1}}^{2}{{\it \_C2}}^{2}+2\,{{\it \_C1}}^{2}{\it \_C2} \,x+{{\it \_C1}}^{2}{x}^{2}+a \right ) }},y \left ( x \right ) =-{\frac { 1}{{\it \_C1}}\sqrt {{\it \_C1}\, \left ( {{\it \_C1}}^{2}{{\it \_C2}}^ {2}+2\,{{\it \_C1}}^{2}{\it \_C2}\,x+{{\it \_C1}}^{2}{x}^{2}+a \right ) }} \right \} \]