4.12.46 \(y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\)

ODE
\[ y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3 \] ODE Classification

[[_Abel, `2nd type``class C`]]

Book solution method
Abel ODE, Second kind

Mathematica
cpu = 911.677 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 4.27 (sec), leaf count = 0 , could not solve

dsolve((g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3, y(x),'implicit')

Mathematica raw input

DSolve[(g0[x] + g1[x]*y[x])*y'[x] == f0[x] + f1[x]*y[x] + f2[x]*y[x]^2 + f3[x]*y[x]^3,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve((g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3, y(x),'implicit')

Maple raw output

dsolve((g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x
)^3, y(x),'implicit')