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

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

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica
cpu = 0.301906 (sec), leaf count = 54

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

Maple
cpu = 0.021 (sec), leaf count = 30

$\left [x -\left (\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{3} \mathit {a3} +\textit {\_a}^{2} \mathit {a2} +\textit {\_a} \mathit {a1} +\mathit {a0}}d \textit {\_a} \right )+\textit {\_C1} = 0\right ]$ 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))

Maple raw output

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