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 = 0.221935 (sec), leaf count = 35
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {x (2+c_1 x)}}\right \},\left \{y(x)\to \frac {1}{\sqrt {x (2+c_1 x)}}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 31
\[\left [y \left (x \right ) = \frac {1}{\sqrt {x^{2} \textit {\_C1} +2 x}}, y \left (x \right ) = -\frac {1}{\sqrt {x^{2} \textit {\_C1} +2 x}}\right ]\] 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))
Maple raw output
[y(x) = 1/(_C1*x^2+2*x)^(1/2), y(x) = -1/(_C1*x^2+2*x)^(1/2)]