ODE
\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)=y(x)^3 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 24.9741 (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 = 1.043 (sec), leaf count = 775
\[\left [y \left (x \right ) = \RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_f}^{8}-\textit {\_C1} \,\textit {\_f}^{2}+\left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {2}{3}}}{\left (-\textit {\_f}^{6}+\textit {\_C1} \right ) \left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {1}{3}}}d \textit {\_f} \right ) a +\textit {\_C2} a +{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}, y \left (x \right ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {-i \sqrt {3}\, \textit {\_f}^{8}+\textit {\_f}^{8}+i \sqrt {3}\, \textit {\_C1} \,\textit {\_f}^{2}+i \sqrt {3}\, \left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {2}{3}}-\textit {\_C1} \,\textit {\_f}^{2}+\left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {2}{3}}}{\left (-\textit {\_f}^{6}+\textit {\_C1} \right ) \left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {1}{3}}}d \textit {\_f} \right ) a +2 \textit {\_C2} a +2 \,{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}, y \left (x \right ) = \RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {-i \sqrt {3}\, \textit {\_f}^{8}-\textit {\_f}^{8}+i \sqrt {3}\, \textit {\_C1} \,\textit {\_f}^{2}+i \sqrt {3}\, \left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {2}{3}}+\textit {\_C1} \,\textit {\_f}^{2}-\left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {2}{3}}}{\left (-\textit {\_f}^{6}+\textit {\_C1} \right ) \left (-\textit {\_f}^{12}+2 \textit {\_C1} \,\textit {\_f}^{6}-\textit {\_C1}^{2}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_f}^{12}-2 \sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1} \,\textit {\_f}^{6}+\sqrt {\frac {\textit {\_C1}}{-\textit {\_f}^{6}+\textit {\_C1}}}\, \textit {\_C1}^{2}\right )^{\frac {1}{3}}}d \textit {\_f} \right ) a +2 \textit {\_C2} a +2 \,{\mathrm e}^{-a x}\right ) {\mathrm e}^{-a x}\right ]\] Mathematica raw input
DSolve[2*a^2*y[x] + a*y[x]^2 + (3*a + y[x])*y'[x] + y''[x] == y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> Piecewise[{{(C[1]*WeierstrassPPrime[x*C[1] + C[2], {0, 1}])/WeierstrassP[x*C[1] + C[2], {0, 1}], a == 0}}, -((C[1]*WeierstrassPPrime[C[1]/(a*E^(a*x)) + C[2], {0, 1}])/(E^(a*x)*WeierstrassP[C[1]/(a*E^(a*x)) + C[2], {0, 1}]))]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+(3*a+y(x))*diff(y(x),x)+2*a^2*y(x)+a*y(x)^2 = y(x)^3, y(x))
Maple raw output
[y(x) = RootOf(Intat((_f^8-_C1*_f^2+(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(2/3))/(-_f^6+_C1)/(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(1/3),_f = _Z)*a+_C2*a+exp(-a*x))/exp(a*x), y(x) = RootOf(-Intat((-I*3^(1/2)*_f^8+_f^8+I*3^(1/2)*_C1*_f^2+I*3^(1/2)*(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(2/3)-_C1*_f^2+(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(2/3))/(-_f^6+_C1)/(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(1/3),_f = _Z)*a+2*_C2*a+2*exp(-a*x))/exp(a*x), y(x) = RootOf(Intat((-I*3^(1/2)*_f^8-_f^8+I*3^(1/2)*_C1*_f^2+I*3^(1/2)*(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(2/3)+_C1*_f^2-(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(2/3))/(-_f^6+_C1)/(-_f^12+2*_C1*_f^6-_C1^2+(_C1/(-_f^6+_C1))^(1/2)*_f^12-2*(_C1/(-_f^6+_C1))^(1/2)*_C1*_f^6+(_C1/(-_f^6+_C1))^(1/2)*_C1^2)^(1/3),_f = _Z)*a+2*_C2*a+2*exp(-a*x))/exp(a*x)]