\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a \left ( y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 2.336797 (sec), leaf count = 242 \[ \left \{\left \{y(x)\to -\frac {\sqrt [4]{2} \sqrt {c_1} \sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}} \text {sn}\left (\left .\frac {(-1)^{3/4} \sqrt {\sqrt {2} \sqrt {a} \sqrt {c_1} x^2+2 \sqrt {2} \sqrt {a} \sqrt {c_1} c_2 x+\sqrt {2} \sqrt {a} \sqrt {c_1} c_2^2}}{\sqrt {2}}\right |-1\right )}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt [4]{2} \sqrt {c_1} \sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}} \text {sn}\left (\left .\frac {(-1)^{3/4} \sqrt {\sqrt {2} \sqrt {a} \sqrt {c_1} x^2+2 \sqrt {2} \sqrt {a} \sqrt {c_1} c_2 x+\sqrt {2} \sqrt {a} \sqrt {c_1} c_2^2}}{\sqrt {2}}\right |-1\right )}{\sqrt {a}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) ={\it \_C2}\,{\it JacobiSN} \left ( \left ( {\frac {x}{2}\sqrt {-2\,a}}+{\it \_C1} \right ) {\it \_C2},i \right ) \right \} \]