ODE
\[ y(x) \left (a+b x^n y(x)\right )+x y'(x)=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.346267 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {a-n}{-b x^n+c_1 (a-n) x^a}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {a -n}{x^{a} \textit {\_C1} a -x^{a} \textit {\_C1} n -b \,x^{n}}\right ]\] Mathematica raw input
DSolve[y[x]*(a + b*x^n*y[x]) + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (a - n)/(-(b*x^n) + (a - n)*x^a*C[1])}}
Maple raw input
dsolve(x*diff(y(x),x)+(a+b*x^n*y(x))*y(x) = 0, y(x))
Maple raw output
[y(x) = (a-n)/(x^a*_C1*a-x^a*_C1*n-b*x^n)]