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 = 0.285737 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {2 x}{x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {2 x}{x^{2}+2 \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = 2*x/(x^2+2*_C1)]