a. Explanation The given differential equation is h ′ ( t ) = − k h . Separate the both side of the equation. d h d t = − k h d h h = − k d t Integrate both side of the above equation. ∫ h ( − 1 2 ) d h = − ∫ k d t h ( − 1 2 + 1 ) ( − 1 2 + 1 ) = − k t + C 1 h 1 2 ( 1 2 ) = − k t + C 1 2 h 1 2 = − k t + C 1 On further simplification, h 1 2 = − k t + C 1 2 b. To determine To find: The solution for k = 0.1 and H = 0.5 m . c. To determine To find: The time taken to drain the tank. d. To determine To sketch: The graph for the solution h = ( 0.7071 − 0.05 t ) 2 .

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

3rd Edition

ISBN: 9780135243435

Author: Bill Briggs

Publisher: Pearson Education (US)

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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 9.3, Problem 49E

To determine

To find: The solution of the initial value problem h′(t)=−kh.

To determine

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

To determine

To find: The time taken to drain the tank.

To determine

To sketch: The graph for the solution h=(0.7071−0.05t)2.

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Chapter 9.3, Problem 48E

Chapter 9.3, Problem 50E

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MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - The solution to the initial value problem y(t) = 2...

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T o find: The solution of the initial value problem h ′ ( t ) = − k h .

Solution Summary: The author explains that the initial value problem is h=(sqrtH)2. Separate the two sides of the equation.

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To find: The solution of the initial value problem h′(t)=−kh.

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

To find: The time taken to drain the tank.

To sketch: The graph for the solution h=(0.7071−0.05t)2.

Want to see the full answer?

Chapter 9 Solutions