4.15.22 $y^{\prime }(x)(a(y(x)+x)+1{)}^n+a(y(x)+x{)}^n=0$

ODE
$$y^{\prime }(x)(a(y(x)+x)+1{)}^n+a(y(x)+x{)}^n=0$$ ODE Classification

[[_homogeneous, `class C`], _dAlembert]

Book solution method
Exact equation

Mathematica ✗
cpu = 599.993 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.123 (sec), leaf count = 40

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

DSolve[a*(x + y[x])^n + (1 + a*(x + y[x]))^n*y'[x] == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve((1+a*(x+y(x)))^n*diff(y(x),x)+a*(x+y(x))^n = 0, y(x),'implicit')

Maple raw output

x+Intat((_a*a+1)^n/(a*_a^n-(_a*a+1)^n),_a = x+y(x))-_C1 = 0