Question

Let $y_c:\R \rightarrow(0,\infin)$ be the solution of the Bernoulli’s equation
$\frac{dy}{dx}-y+y^3=0,\ \ \ \ \ \ \ y(0)=c \gt 0.$
Then, for every 𝑐 > 0, which one of the following is true ?

• A. $\lim\limits_{x\rightarrow \infin}y_c(x)=0$
• B. $\lim\limits_{x\rightarrow \infin}y_c(x)=1$
• C. $\lim\limits_{x\rightarrow \infin}y_c(x)=e$
• D. $\lim\limits_{x\rightarrow \infin}y_c(x)$ does not exist

Answer 1

Answer: (B)

$\lim\limits_{x\rightarrow \infin}y_c(x)=1$

Answer 2

The correct option is (B) : $\lim\limits_{x\rightarrow \infin}y_c(x)=1$.