\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\, \left ( y \left ( x \right ) \right ) ^{3}+2\,{a}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 1.489689 (sec), leaf count = 31 \[ \text {DSolve}\left [2 a^2 y(x)+3 a y'(x)+y''(x)-2 y(x)^3=0,y(x),x\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{{{\rm e}^{ax}}}{\it JacobiSN} \left ( \left ( -{\frac {1}{a}\sqrt {-{{\rm e}^{-2\,ax}}}}+{ \it \_C1} \right ) {\it \_C2},i \right ) } \right \} \]