4.15.22 \(y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0\)

ODE
\[ y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0 \] 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

\[ \left \{ x+\int ^{x+y \relax (x ) }\!{\frac { \left ({\it \_a}\,a+1 \right ) ^{n}}{a{{\it \_a}}^{n}- \left ({\it \_a}\,a+1 \right ) ^{n}}}{d{\it \_a}}-{\it \_C1}=0 \right \} \] 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