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

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

[_Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0129408 (sec), leaf count = 45

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

Maple
cpu = 0.006 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{-2}-x-{\frac {1}{2}}-{{\rm e}^{2\,x}}{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)^2-x-1/2-exp(2*x)*_C1 = 0