ODE
\[ y'(x)+y(x) \left (1-x y(x)^2\right )=0 \] ODE Classification
[_Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.221357 (sec), leaf count = 45
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}}\right \},\left \{y(x)\to \frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 39
\[\left [y \left (x \right ) = -\frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} \textit {\_C1} +4 x}}, y \left (x \right ) = \frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} \textit {\_C1} +4 x}}\right ]\] Mathematica raw input
DSolve[y[x]*(1 - x*y[x]^2) + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(1/Sqrt[1/2 + x + E^(2*x)*C[1]])}, {y[x] -> 1/Sqrt[1/2 + x + E^(2*x)*C[1]]}}
Maple raw input
dsolve(diff(y(x),x)+y(x)*(1-x*y(x)^2) = 0, y(x))
Maple raw output
[y(x) = -2/(2+4*exp(2*x)*_C1+4*x)^(1/2), y(x) = 2/(2+4*exp(2*x)*_C1+4*x)^(1/2)]