4.4.26 \(x y'(x)=y(x) (1-x y(x))\)

ODE
\[ x y'(x)=y(x) (1-x y(x)) \] ODE Classification

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00669308 (sec), leaf count = 18

\[\left \{\left \{y(x)\to \frac {2 x}{2 c_1+x^2}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 17

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-{\frac {x}{2}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] Mathematica raw input

DSolve[x*y'[x] == y[x]*(1 - x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> (2*x)/(x^2 + 2*C[1])}}

Maple raw input

dsolve(x*diff(y(x),x) = (1-x*y(x))*y(x), y(x),'implicit')

Maple raw output

1/y(x)-1/2*x-1/x*_C1 = 0