4.36.42 $2a^{2}y(x)+(3a+y(x))y^{\prime }(x)+ay(x{)}^2+y^{″}(x)=y(x{)}^3$

ODE
$$2a^{2}y(x)+(3a+y(x))y^{\prime }(x)+ay(x{)}^2+y^{″}(x)=y(x{)}^3$$ 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

$$\{\frac{1}{a}(-{\mathrm{e}}^{-ax}+(-{\int }^{y\left(x\right){\mathrm{e}}^{ax}}\frac{1}{2{\mathit{\_}\mathit{f}}^6-2\mathit{\_}\mathit{C}\mathit{1}}(-{\mathit{\_}\mathit{f}}^2(i\sqrt{3}-1)({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})}}+\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})}(i\sqrt{3}+1))d\mathit{\_}\mathit{f}-\mathit{\_}\mathit{C}\mathit{2})a)=0,\frac{1}{a}(-{\mathrm{e}}^{-ax}+(-{\int }^{y\left(x\right){\mathrm{e}}^{ax}}\frac{1}{2{\mathit{\_}\mathit{f}}^6-2\mathit{\_}\mathit{C}\mathit{1}}({\mathit{\_}\mathit{f}}^2(i\sqrt{3}+1)({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})}}+(-i\sqrt{3}+1)\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})})d\mathit{\_}\mathit{f}-\mathit{\_}\mathit{C}\mathit{2})a)=0,\frac{1}{a}(-{\mathrm{e}}^{-ax}+(-{\int }^{y\left(x\right){\mathrm{e}}^{ax}}\frac{1}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})}-{\mathit{\_}\mathit{f}}^2\frac{1}{\sqrt[3]{{({\mathit{\_}\mathit{f}}^6-\mathit{\_}\mathit{C}\mathit{1})}^2(-1+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}})}}d\mathit{\_}\mathit{f}-\mathit{\_}\mathit{C}\mathit{2})a)=0\}$$ 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