4.4.27 \(x y'(x)=y(x) (x y(x)+1)\)

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

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00687323 (sec), leaf count = 18

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

Maple
cpu = 0.005 (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