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