4.4.25 \(x y'(x)+y(x) (1-x y(x))=0\)

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

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}- \left (-\ln \relax (x ) +{\it \_C1} \right ) x=0 \right \} \] 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