(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

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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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 .

Want to see the full answer?

Chapter D1 Solutions