ODE
\[ x y'(x) \left (a+x y(x)^n\right )+b y(x)=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Change of Variable, new independent variable
Mathematica ✓
cpu = 0.577483 (sec), leaf count = 50
\[\text {Solve}\left [\frac {n \left (a \log (y(x) (a-b n))-b \log \left (a-b n+x y(x)^n\right )+b \log (x)\right )}{b n-a}=c_1,y(x)\right ]\]
Maple ✓
cpu = 0.326 (sec), leaf count = 37
\[[\left (y \left (x \right )^{n}\right )^{a} \left (x y \left (x \right )^{n}-b n +a \right )^{-b n} x^{b n}-\textit {\_C1} = 0]\] 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))
Maple raw output
[(y(x)^n)^a/((x*y(x)^n-b*n+a)^(b*n))*x^(b*n)-_C1 = 0]