4.4.30 \(x y'(x)=y(x) (2 x y(x)+1)\)

ODE
\[ x y'(x)=y(x) (2 x y(x)+1) \] ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00724698 (sec), leaf count = 18

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

Maple
cpu = 0.005 (sec), leaf count = 15

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

DSolve[x*y'[x] == y[x]*(1 + 2*x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -(x/(x^2 - C[1]))}}

Maple raw input

dsolve(x*diff(y(x),x) = y(x)*(1+2*x*y(x)), y(x),'implicit')

Maple raw output

x-1/x*_C1+1/y(x) = 0