Explanation Given: The differential equation is y ′ ( t ) = 0.05 ( y + 1 ) 2 ( t − 1 ) 2 , | t | ≤ 3 and | y | ≤ 3 . Graph: The graph of the function y ′ ( t ) = 0.05 ( y + 1 ) 2 ( t − 1 ) 2 is shown below in figure 1. Observation : From Figure 1, it is observed that the horizontal line segments represents the equilibrium solution at y = − 1 . Explanation: Take the differential equation y ′ ( t ) = 0

Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

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

Publisher: PEARSON

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Chapter D1.2, Problem 9E

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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 D1.2, Problem 8E

Chapter D1.2, Problem 10E

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Chapter D1 Solutions

Calculus: Early Transcendentals, 2nd Edition

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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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.

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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 D1 Solutions