ODE
\[ x (3-x y(x)) y'(x)=y(x) (x y(x)-1) \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 4.95322 (sec), leaf count = 30
\[\left \{\left \{y(x)\to -\frac {3 W\left (e^{\frac {9 c_1}{2^{2/3}}-1} x^{2/3}\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 21
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}+{\frac {xy \left ( x \right ) }{2}}-{\frac {3\,\ln \left ( xy \left ( x \right ) \right ) }{2}}=0 \right \} \] Mathematica raw input
DSolve[x*(3 - x*y[x])*y'[x] == y[x]*(-1 + x*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (-3*ProductLog[E^(-1 + (9*C[1])/2^(2/3))*x^(2/3)])/x}}
Maple raw input
dsolve(x*(3-x*y(x))*diff(y(x),x) = y(x)*(x*y(x)-1), y(x),'implicit')
Maple raw output
ln(x)-_C1+1/2*x*y(x)-3/2*ln(x*y(x)) = 0