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 = 0.0391074 (sec), leaf count = 54

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

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

\[ \left \{ x-\int ^{y \relax (x ) }\! \left ({{\it \_a}}^{3}{\it a3}+{{\it \_a}}^{2}{\it a2}+{\it \_a}\,{\it a1}+{\it a0} \right ) ^{-1}{d{\it \_a}}+{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

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