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12. Consider the differential equation y' = y-y . Which of the following statements is/are true? O This differential equation has infinitely many solutions. The constant function f(t) = 1 is a solution to this differential equation. %3D The function f(t) =- 1 is a solution to this differential equation with initial condition v(0) = %3D %3D (1+e-) If f(t) is a solution to the differential equation satisfying the initial condition y(0) = 0, then f '(0) = O All of these statements are true. A Moving to the next question prevents changes to this answer.

12. Consider the differential equation y' = y-y . Which of the following statements is/are true? O This differential equation has infinitely many solutions. The constant function f(t) = 1 is a solution to this differential equation. %3D The function f(t) =- 1 is a solution to this differential equation with initial condition v(0) = %3D %3D (1+e-) If f(t) is a solution to the differential equation satisfying the initial condition y(0) = 0, then f '(0) = O All of these statements are true. A Moving to the next question prevents changes to this answer.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question 10** Consider the differential equation \( y' = y - y^2 \). Which of the following statements is/are true? - A) This differential equation has infinitely many solutions. - B) The constant function \( f(t) = 1 \) is a solution to this differential equation. - C) The function \( f(t) = \frac{1}{1 + e^{-t}} \) is a solution to this differential equation with initial condition \( y(0) = \frac{1}{2} \). - D) If \( f(t) \) is a solution to the differential equation satisfying the initial condition \( y(0) = 0 \), then \( f'(0) = 0 \). - E) All of these statements are true. **Note:** Moving to the next question prevents changes to this answer. --- This question tests your understanding of differential equations and solution characteristics. Review each statement carefully to determine its validity based on the given differential equation.
Transcribed Image Text:**Question 10** Consider the differential equation \( y' = y - y^2 \). Which of the following statements is/are true? - A) This differential equation has infinitely many solutions. - B) The constant function \( f(t) = 1 \) is a solution to this differential equation. - C) The function \( f(t) = \frac{1}{1 + e^{-t}} \) is a solution to this differential equation with initial condition \( y(0) = \frac{1}{2} \). - D) If \( f(t) \) is a solution to the differential equation satisfying the initial condition \( y(0) = 0 \), then \( f'(0) = 0 \). - E) All of these statements are true. **Note:** Moving to the next question prevents changes to this answer. --- This question tests your understanding of differential equations and solution characteristics. Review each statement carefully to determine its validity based on the given differential equation.
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