a. Explanation Given: The free fall of an object in a gravitational field subject to air resistance uses the differential equation v ′ ( t ) = g − b v . Where v ( t ) is the velocity of the object for t ≥ 0 , g = 9.8 m / s 2 is the acceleration due to gravity, and b ≥ 0 is a constant that involves the mass of the object and the air resistance b. To determine To find: The initial value v ( 0 ) = A , when the solutions are increasing or decreasing. c. To determine To find: The equilibrium solution of the differential equation.

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 47E

To determine

To draw: The direction field on the region 0≤t≤60 and 0≤y≤150 .

To determine

To find: The initial value v(0)=A , when the solutions are increasing or decreasing.

To determine

To find: The equilibrium solution of the differential equation.

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Chapter D1.2, Problem 46E

Chapter D1.2, Problem 48E

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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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To draw: The direction field on the region 0 ≤ t ≤ 60 and 0 ≤ y ≤ 150 .

Solution Summary: The author explains how to draw the direction field using the differential equation vprime(t)=g-bv.

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To draw: The direction field on the region 0≤t≤60 and 0≤y≤150 .

To find: The initial value v(0)=A , when the solutions are increasing or decreasing.

To find: The equilibrium solution of the differential equation.

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Chapter D1 Solutions