4.15.23 $x{y}^{\prime }(x)(a+xy(x{)}^n)+by(x)=0$

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

[[_homogeneous, `class G`], _rational]

Book solution method
Change of Variable, new independent variable

Mathematica ✓
cpu = 0.164489 (sec), leaf count = 50

$$\text{Solve}[\frac{n(a\log (y(x)(a-bn))-b\log (a-bn+xy(x{)}^n)+b\log (x))}{bn-a}=c_1,y(x)]$$

Maple ✓
cpu = 0.085 (sec), leaf count = 37

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

(y(x)^n)^a/((x*y(x)^n-b*n+a)^(b*n))*x^(b*n)-_C1 = 0