ODE
\[ x y'(x)+y(x) (1-x y(x))=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00701563 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {1}{c_1 x-x \log (x)}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 17
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{-1}- \left ( -\ln \left ( x \right ) +{\it \_C1} \right ) x=0 \right \} \] Mathematica raw input
DSolve[y[x]*(1 - x*y[x]) + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1] - x*Log[x])^(-1)}}
Maple raw input
dsolve(x*diff(y(x),x)+(1-x*y(x))*y(x) = 0, y(x),'implicit')
Maple raw output
1/y(x)-(-ln(x)+_C1)*x = 0