\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 24.3607 (sec), leaf count = 88
\[\left \{\left \{y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {c_1 \wp '(x c_1+c_2;0,1)}{\wp (x c_1+c_2;0,1)} & a=0 \\ -\frac {e^{-a x} c_1 \wp '\left (\frac {e^{-a x} c_1}{a}+c_2;0,1\right )}{\wp \left (\frac {e^{-a x} c_1}{a}+c_2;0,1\right )} & \text {True} \\\end {array} \\\end {array}\right \}\right \}\] ✓ Maple : cpu = 1.829 (sec), leaf count = 817
\[\left \{y \left (x \right ) = \RootOf \left (c_{2} a +a \left (\int _{}^{\textit {\_Z}}\frac {-\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} \textit {\_f}^{6}+\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} c_{1}^{2}-\textit {\_f}^{2}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right ) \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {1}{3}}}d \textit {\_f} \right )+{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}, y \left (x \right ) = \RootOf \left (2 c_{2} a -a \left (\int _{}^{\textit {\_Z}}\frac {-i \sqrt {3}\, \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} \textit {\_f}^{6}-\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} \textit {\_f}^{6}+i \sqrt {3}\, \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} c_{1}^{2}+\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} c_{1}^{2}+i \sqrt {3}\, \textit {\_f}^{2}-\textit {\_f}^{2}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right ) \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {1}{3}}}d \textit {\_f} \right )+2 \,{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}, y \left (x \right ) = \RootOf \left (2 c_{2} a +a \left (\int _{}^{\textit {\_Z}}\frac {-i \sqrt {3}\, \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} \textit {\_f}^{6}+\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} \textit {\_f}^{6}+i \sqrt {3}\, \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} c_{1}^{2}-\left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {2}{3}} c_{1}^{2}+i \sqrt {3}\, \textit {\_f}^{2}+\textit {\_f}^{2}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right ) \left (-\frac {-c_{1} \textit {\_f}^{12}+2 c_{1}^{3} \textit {\_f}^{6}-c_{1}^{5}+\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {5}{2}}}{\left (-\textit {\_f}^{6}+c_{1}^{2}\right )^{\frac {7}{2}}}\right )^{\frac {1}{3}}}d \textit {\_f} \right )+2 \,{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}\right \}\]