4.1117   ay′(x)+ y′(x)n = by(x)

ODE

ay′(x)+ y′(x )n = by(x )

ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for y

Mathematica
cpu = 0.293822 (sec), leaf count = 46

    [{                                                               }                ]
           alog(K$201926) + nK$20n1−9126n−1-          aK$201926 + K$201926n
Solve   x = ------------b--------------+c1,y(x) =----------b----------  ,{y(x),K$201926}

Maple
cpu = 0.046 (sec), leaf count = 33

{    ∫ y(x)                                              }
 x −      (RootOf ( Zn + a-Z − b a))−1d-a−-C1 = 0,y (x ) = 0

Mathematica raw input

DSolve[a*y'[x] + y'[x]^n == b*y[x],y[x],x]

Mathematica raw output

Solve[{x == C[1] + ((K$201926^(-1 + n)*n)/(-1 + n) + a*Log[K$201926])/b, y[x] ==
 (a*K$201926 + K$201926^n)/b}, {y[x], K$201926}]

Maple raw input

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

Maple raw output

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