(a) Explanation Given: The Differential equation is h ′ ( t ) = − 2 k h . Calculation: The differential equation is h ′ ( t ) = − 2 k h . Separate the both side of the equation. d h d t = − 2 k h d h − 2 h = k d t Integrate both side of the above equation. ∫ d h 2 h = − ∫ k d t 1 2 d h h − 1 2 = − k t + c 1 2 h 1 2 1 2 = − k t + c h 1 2 = − k t + c Simplify further as follows (b) To determine To find: The solution for k = 0.1 and H = 0.5 . (c) To determine To find: The time taken to drain the tank. (d) To determine To sketch: Graph for the solution h = ( 0.7071 − 0.1 t ) 2 .

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Differential Equations

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Chapter D1.3, Problem 47E

(a)

To determine

To Find: The solution of the given initial value problem.

(b)

To determine

To find: The solution for k=0.1 and H=0.5 .

(c)

To determine

To find: The time taken to drain the tank.

(d)

To determine

To sketch: Graph for the solution h=(0.7071−0.1t)2 .

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Chapter D1.3, Problem 46E

Chapter D1.3, Problem 48E

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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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T o Find: The solution of the given initial value problem.

Solution Summary: The author explains how to find the solution of the given initial value problem.

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To Find: The solution of the given initial value problem.

To find: The solution for k=0.1 and H=0.5 .

To find: The time taken to drain the tank.

To sketch: Graph for the solution h=(0.7071−0.1t)2 .

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Chapter D1 Solutions