4.2.32 $y^{\prime }(x)=\text{a0}+\text{a1}y(x)+\text{a2}y(x{)}^2+\text{a3}y(x{)}^3$

ODE
$$y^{\prime }(x)=\text{a0}+\text{a1}y(x)+\text{a2}y(x{)}^2+\text{a3}y(x{)}^3$$ ODE Classification

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica ✓
cpu = 0.0391074 (sec), leaf count = 54

$$\text{Solve}[c_1+x=\text{RootSum}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},\frac{\log (y(x)-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2\text{a3}+2\mathrm{\#}\text{1}\text{a2}+\text{a1}}\mathrm{\&}],y(x)]$$

Maple ✓
cpu = 0.019 (sec), leaf count = 30

$$\{x-{\int }^{y\left(x\right)}{({\mathit{\_}\mathit{a}}^3\mathit{a}\mathit{3}+{\mathit{\_}\mathit{a}}^2\mathit{a}\mathit{2}+\mathit{\_}\mathit{a}\mathit{a}\mathit{1}+\mathit{a}\mathit{0})}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[y'[x] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^3,y[x],x]

Mathematica raw output

Solve[x + C[1] == RootSum[a0 + a1*#1 + a2*#1^2 + a3*#1^3 & , Log[-#1 + y[x]]/(a1
 + 2*a2*#1 + 3*a3*#1^2) & ], y[x]]

Maple raw input

dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3, y(x),'implicit')

Maple raw output

x-Intat(1/(_a^3*a3+_a^2*a2+_a*a1+a0),_a = y(x))+_C1 = 0