Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

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

Publisher: PEARSON

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Differential Equations

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Chapter D1.2, Problem 38E

Equilibrium solutions A differential equation of the form y′(t) = f(y) is said to be autonomous (the function f depends only on y). The constant function y = y₀ is an equilibrium solution of the equation provided f(y₀) = 0 (because then y′(t) = 0 and the solution remains constant for all t). Note that equilibrium solutions correspond to horizontal lines in the direction field. Note also that for autonomous equations, the direction field is independent of t. Carry out the following analysis on the given equations.

a. Find the equilibrium solutions.
b. Sketch the direction field, for t ≥ 0.
c. Sketch the solution curve that corresponds to the initial condition y (0) = 1.

38. y′(t) = 2y + 4

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Chapter D1.2, Problem 37E

Chapter D1.2, Problem 39E

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Chapter D1 Solutions

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

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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Solution Summary: The author explains that the equilibrium solution of the given differential equation is y(t)=2y+4.

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