\[ y''(x)-a y(x)^3=0 \] ✓ Mathematica : cpu = 1.76122 (sec), leaf count = 242
DSolve[-(a*y[x]^3) + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt [4]{2} \sqrt {c_1} \sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}} \text {sn}\left (\left .\frac {(-1)^{3/4} \sqrt {\sqrt {2} \sqrt {a} \sqrt {c_1} x^2+2 \sqrt {2} \sqrt {a} \sqrt {c_1} c_2 x+\sqrt {2} \sqrt {a} \sqrt {c_1} c_2{}^2}}{\sqrt {2}}\right |-1\right )}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt [4]{2} \sqrt {c_1} \sqrt {\frac {i \sqrt {a}}{\sqrt {c_1}}} \text {sn}\left (\left .\frac {(-1)^{3/4} \sqrt {\sqrt {2} \sqrt {a} \sqrt {c_1} x^2+2 \sqrt {2} \sqrt {a} \sqrt {c_1} c_2 x+\sqrt {2} \sqrt {a} \sqrt {c_1} c_2{}^2}}{\sqrt {2}}\right |-1\right )}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.783 (sec), leaf count = 21
dsolve(diff(diff(y(x),x),x)-a*y(x)^3=0,y(x))
\[y \left (x \right ) = c_{2} \mathrm {sn}\left (\left (\frac {\sqrt {-2 a}\, x}{2}+c_{1}\right ) c_{2}| i\right )\]