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 = 0.230706 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {1}{-x \log (x)+c_1 x}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 17
\[\left [y \left (x \right ) = -\frac {1}{\left (\ln \left (x \right )-\textit {\_C1} \right ) x}\right ]\] 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))
Maple raw output
[y(x) = -1/(ln(x)-_C1)/x]