Explanation Given: The differential equation is y ′ ( t ) = ( y − 1 ) sin π t , where 0 ≤ t ≤ 2 and 0 ≤ y ≤ 2 . Calculation: The graph of the differential equation y ′ ( t ) = ( y − 1 ) sin π t is shown below in Figure 1. From Figure 1 it is observed that the horizontal line segments represents the equilibrium solution at y ( 0 ) = 1

Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

3rd Edition

ISBN: 9780134995991

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 9.2, Problem 10E

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To find: The initial condition for y(0)=A lead to the solution increasing in time and to find the constant solution with graph.

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Chapter 9.2, Problem 9E

Chapter 9.2, Problem 11E

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Chapter 9 Solutions

Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - What is the solution of the initial value problem...Ch. 9.1 - Solve the initial value problem in Example 4a with...Ch. 9.1 - Suppose the initial conditions in Example 5a are...Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Consider the differential equation y(t) + 9y(t) =...Ch. 9.1 - If the general solution of a differential equation...Ch. 9.1 - Does the function y(t) = 2t satisfy the...Ch. 9.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. 9.1 - The solution to the initial value problem y(t) = 2...

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The initial condition for y ( 0 ) = A lead to the solution increasing in time and to find the constant solution with graph.

Solution Summary: The author explains that the initial condition for y(0)=A leads to the solution increasing in time and to find the constant solution with graph.