\[ y''(x)-a y(x)^3=0 \] ✓ Mathematica : cpu = 2.30253 (sec), leaf count = 131
\[\left \{\left \{y(x)\to -\frac {i \sqrt [4]{2} \text {sn}\left (\left .-\frac {(1-i) \sqrt {\sqrt {a} \sqrt {c_1} \left (x+c_2\right ){}^2}}{2^{3/4}}\right |-1\right )}{\sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}}}\right \},\left \{y(x)\to \frac {i \sqrt [4]{2} \text {sn}\left (\left .-\frac {(1-i) \sqrt {\sqrt {a} \sqrt {c_1} \left (x+c_2\right ){}^2}}{2^{3/4}}\right |-1\right )}{\sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}}}\right \}\right \}\]
✓ Maple : cpu = 0.054 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{\it JacobiSN} \left ( \left ( {\frac {x}{2}\sqrt {-2\,a}}+{\it \_C1} \right ) {\it \_C2},i \right ) \right \} \]