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 = 0.0261589 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {a-n}{c_1 (a-n) x^a-b x^n}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 26
\[ \left \{ {\frac {b{x}^{n}}{a-n}}-{x}^{a}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] 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),'implicit')
Maple raw output
1/(a-n)*x^n*b-x^a*_C1+1/y(x) = 0