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 = 26.101 (sec), leaf count = 0 , could not solve
DSolve[2*a^2*y[x] + a*y[x]^2 + (3*a + y[x])*Derivative[1][y][x] + Derivative[2][y][x] == y[x]^3, y[x], x]
Maple ✓
cpu = 0.293 (sec), leaf count = 358
\[ \left \{ {\frac {1}{a} \left ( -{{\rm e}^{-ax}}+ \left ( -\int ^{y \left ( x \right ) {{\rm e}^{ax}}}\!{\frac {1}{2\,{{\it \_f}}^{6}-2\,{\it \_C1}} \left ( -{{{\it \_f}}^{2} \left ( i\sqrt {3}-1 \right ) \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) {\frac {1}{\sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) }}}}+\sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) } \left ( i\sqrt {3}+1 \right ) \right ) }{d{\it \_f}}-{\it \_C2} \right ) a \right ) }=0,{\frac {1}{a} \left ( -{{\rm e}^{-ax}}+ \left ( -\int ^{y \left ( x \right ) {{\rm e}^{ax}}}\!{\frac {1}{2\,{{\it \_f}}^{6}-2\,{\it \_C1}} \left ( {{{\it \_f}}^{2} \left ( i\sqrt {3}+1 \right ) \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) {\frac {1}{\sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) }}}}+ \left ( -i\sqrt {3}+1 \right ) \sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) } \right ) }{d{\it \_f}}-{\it \_C2} \right ) a \right ) }=0,{\frac {1}{a} \left ( -{{\rm e}^{-ax}}+ \left ( -\int ^{y \left ( x \right ) {{\rm e}^{ax}}}\!{\frac {1}{-{{\it \_f}}^{6}+{\it \_C1}}\sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) }}-{{{\it \_f}}^{2}{\frac {1}{\sqrt [3]{ \left ( {{\it \_f}}^{6}-{\it \_C1} \right ) ^{2} \left ( -1+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}} \right ) }}}}{d{\it \_f}}-{\it \_C2} \right ) a \right ) }=0 \right \} \] 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
DSolve[2*a^2*y[x] + a*y[x]^2 + (3*a + y[x])*Derivative[1][y][x] + Derivative[2][y][x] == y[x]^3, y[x], x]
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),'implicit')
Maple raw output
(-exp(-a*x)+(-Intat(1/(-_f^6+_C1)*((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3)-_f^2/((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3),_f = y(x)*exp(a*x))-_C2)*a)/a = 0, (-exp(-a*x)+(-Intat((-_f^2*(I*3^(1/2)-1)*(_f^6-_C1)/((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3)+((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3)*(I*3^(1/2)+1))/(2*_f^6-2*_C1),_f = y(x)*exp(a*x))-_C2)*a)/a = 0, (-exp(-a*x)+(-Intat((_f^2*(I*3^(1/2)+1)*(_f^6-_C1)/((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3)+(-I*3^(1/2)+1)*((_f^6-_C1)^2*(-1+(_C1/(-_f^6+_C1))^(1/2)))^(1/3))/(2*_f^6-2*_C1),_f = y(x)*exp(a*x))-_C2)*a)/a = 0