Let yc : ℝ → (0, ∞) be the solution of the Bernoulli’s equation
\(\frac{d y}{d x}-y+y^3=0, \quad y(0)=c>0 \)
Then, for every c > 0, which one of the following is true?
1
\(\lim _{x \rightarrow \infty} y_c(x)=0 \)
2
\(\lim _{x \rightarrow \infty} y_c(x)=1 \)
3
\(\lim _{x \rightarrow \infty} y_c(x)=e \)
4
\(\lim _{x \rightarrow \infty} y_c(x)\) does not exist