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 ?
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 ?
\(\frac{dy}{dx}-y+y^3=0,\ \ \ \ \ \ \ y(0)=c \gt 0.\)
Then, for every 𝑐 > 0, which one of the following is true ?
Updated On: Jan 31, 2025
- \(\lim\limits_{x\rightarrow \infin}y_c(x)=0\)
- \(\lim\limits_{x\rightarrow \infin}y_c(x)=1\)
- \(\lim\limits_{x\rightarrow \infin}y_c(x)=e\)
- \(\lim\limits_{x\rightarrow \infin}y_c(x)\) does not exist
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The Correct Option is B
Solution and Explanation
The correct option is (B) : \(\lim\limits_{x\rightarrow \infin}y_c(x)=1\).
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