4.4.41 \(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\)

ODE
\[ x y'(x)+y(x) \left (1-x y(x)^2\right )=0 \] ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00785942 (sec), leaf count = 35

\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {x \left (c_1 x+2\right )}}\right \},\left \{y(x)\to \frac {1}{\sqrt {x \left (c_1 x+2\right )}}\right \}\right \}\]

Maple
cpu = 0.004 (sec), leaf count = 17

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

DSolve[y[x]*(1 - x*y[x]^2) + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(1/Sqrt[x*(2 + x*C[1])])}, {y[x] -> 1/Sqrt[x*(2 + x*C[1])]}}

Maple raw input

dsolve(x*diff(y(x),x)+y(x)*(1-x*y(x)^2) = 0, y(x),'implicit')

Maple raw output

-2*x-x^2*_C1+1/y(x)^2 = 0