\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 23.6609 (sec), leaf count = 88
DSolve[2*a^2*y[x] + a*y[x]^2 - y[x]^3 + (3*a + y[x])*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {c_1 \wp '(x c_1+c_2;0,1)}{\wp (x c_1+c_2;0,1)} & a=0 \\ -\frac {e^{-a x} c_1 \wp '\left (\frac {e^{-a x} c_1}{a}+c_2;0,1\right )}{\wp \left (\frac {e^{-a x} c_1}{a}+c_2;0,1\right )} & \text {True} \\\end {array} \\\end {array}\right \}\right \}\] ✓ Maple : cpu = 1.063 (sec), leaf count = 415
dsolve(diff(diff(y(x),x),x)+(y(x)+3*a)*diff(y(x),x)-y(x)^3+a*y(x)^2+2*a^2*y(x)=0,y(x))
\[y \left (x \right ) = \RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_f}^{8}-c_{1} \textit {\_f}^{2}+\left (\left (-\textit {\_f}^{6}+c_{1}\right )^{2} \left (\sqrt {\frac {c_{1}}{-\textit {\_f}^{6}+c_{1}}}-1\right )\right )^{\frac {2}{3}}}{\left (-\textit {\_f}^{6}+c_{1}\right ) \left (\left (-\textit {\_f}^{6}+c_{1}\right )^{2} \left (\sqrt {\frac {c_{1}}{-\textit {\_f}^{6}+c_{1}}}-1\right )\right )^{\frac {1}{3}}}d \textit {\_f} \right ) a +c_{2} a +{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}\]