ODE
\[ x y'(x) (a+b y(x))=c y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0140668 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {a W\left (\frac {b e^{\frac {c_1}{a}} x^{\frac {c}{a}}}{a}\right )}{b}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 24
\[ \left \{ \ln \left ( x \right ) -{\frac {a\ln \left ( y \left ( x \right ) \right ) }{c}}-{\frac {by \left ( x \right ) }{c}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*(a + b*y[x])*y'[x] == c*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (a*ProductLog[(b*E^(C[1]/a)*x^(c/a))/a])/b}}
Maple raw input
dsolve(x*(a+b*y(x))*diff(y(x),x) = c*y(x), y(x),'implicit')
Maple raw output
ln(x)-1/c*a*ln(y(x))-b/c*y(x)+_C1 = 0