Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion
11th Edition
ISBN: 9781119336617
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley (WileyPLUS Products)
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Question
Chapter 2.1, Problem 5P
(a)
To determine
To sketch: The directional field for the differential equation
(b)
To determine
The behavior of the solution for large values of
(c)
To determine
To solve: The differential equation
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Total marks 16
5.
Let (,,P) be a probability space and let X : → R be a random
variable whose probability density function is given by f(x) = }}|x|e¯|×| for
x Є R.
(i)
(ii)
Find the characteristic function of the random variable X.
[8 Marks]
Using the result of (i), calculate the first two moments of the
random variable X, i.e., E(X") for n = 1, 2.
(iii) What is the variance of X?
[6 Marks]
[2 Marks]
Refer to page 12 for a problem on solving a homogeneous differential equation.
Instructions:
• Simplify the equation into a homogeneous form.
Use appropriate substitutions to reduce complexity.
Solve systematically and verify the final result with clear back-substitutions.
Link:
[https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]
Refer to page 36 for solving a bang-bang control problem.
Instructions:
•
Formulate the problem, identifying the control constraints.
•
•
Apply Pontryagin's Maximum Principle to derive the switching conditions.
Clearly illustrate the switching points in the control trajectory. Verify the solution satisfies the
optimality criteria.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
Chapter 2 Solutions
Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.1 - Prob. 8PCh. 2.1 - Prob. 9PCh. 2.1 - Prob. 10P
Ch. 2.1 - Prob. 11PCh. 2.1 - Prob. 12PCh. 2.1 - Prob. 13PCh. 2.1 - Prob. 14PCh. 2.1 - Prob. 15PCh. 2.1 - Prob. 16PCh. 2.1 - Prob. 17PCh. 2.1 - Prob. 18PCh. 2.1 - Prob. 19PCh. 2.1 - Prob. 20PCh. 2.1 - Prob. 21PCh. 2.1 - Prob. 22PCh. 2.1 - Prob. 23PCh. 2.1 - Prob. 24PCh. 2.1 - Prob. 25PCh. 2.1 - Prob. 26PCh. 2.1 - Prob. 27PCh. 2.1 - Variation of Parameters. Consider the following...Ch. 2.1 - Prob. 29PCh. 2.1 - In each of Problems 29 and 30, use the method of...Ch. 2.2 - Prob. 1PCh. 2.2 - Prob. 2PCh. 2.2 - Prob. 3PCh. 2.2 - Prob. 4PCh. 2.2 - Prob. 5PCh. 2.2 - Prob. 6PCh. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - Prob. 9PCh. 2.2 - Prob. 10PCh. 2.2 - Prob. 11PCh. 2.2 - Prob. 12PCh. 2.2 - Prob. 13PCh. 2.2 - Prob. 14PCh. 2.2 - Prob. 15PCh. 2.2 - Prob. 16PCh. 2.2 - Prob. 17PCh. 2.2 - Prob. 18PCh. 2.2 - Prob. 19PCh. 2.2 - Prob. 20PCh. 2.2 - Prob. 21PCh. 2.2 - Prob. 22PCh. 2.2 - Prob. 23PCh. 2.2 - Prob. 24PCh. 2.2 - Prob. 25PCh. 2.2 - Prob. 26PCh. 2.2 - Prob. 27PCh. 2.2 - Prob. 28PCh. 2.2 - Prob. 29PCh. 2.2 - Prob. 30PCh. 2.2 - Prob. 31PCh. 2.3 - Prob. 1PCh. 2.3 - Prob. 2PCh. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.3 - Prob. 10PCh. 2.3 - Prob. 11PCh. 2.3 - Prob. 12PCh. 2.3 - Prob. 13PCh. 2.3 - Prob. 14PCh. 2.3 - Prob. 15PCh. 2.3 - Prob. 16PCh. 2.3 - Assume that the conditions are as in Problem 16...Ch. 2.3 - Prob. 18PCh. 2.3 - Prob. 19PCh. 2.3 - Prob. 20PCh. 2.3 - Prob. 21PCh. 2.3 - Prob. 22PCh. 2.3 - Prob. 23PCh. 2.3 - Prob. 24PCh. 2.4 - In each of Problems 1 through 6, determine...Ch. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 13PCh. 2.4 - Prob. 14PCh. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Prob. 20PCh. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Prob. 27PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 16PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2.5 - Prob. 20PCh. 2.5 - Prob. 21PCh. 2.5 - Prob. 22PCh. 2.5 - Prob. 23PCh. 2.5 - Prob. 24PCh. 2.5 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2.6 - Prob. 5PCh. 2.6 - Prob. 6PCh. 2.6 - Prob. 7PCh. 2.6 - Prob. 8PCh. 2.6 - Prob. 9PCh. 2.6 - Prob. 10PCh. 2.6 - Prob. 11PCh. 2.6 - Prob. 12PCh. 2.6 - Prob. 13PCh. 2.6 - Prob. 14PCh. 2.6 - Prob. 15PCh. 2.6 - Prob. 16PCh. 2.6 - Prob. 17PCh. 2.6 - Prob. 18PCh. 2.6 - Prob. 19PCh. 2.6 - Prob. 20PCh. 2.6 - Prob. 21PCh. 2.6 - Prob. 22PCh. 2.7 - Prob. 1PCh. 2.7 - Prob. 2PCh. 2.7 - Prob. 3PCh. 2.7 - Prob. 4PCh. 2.7 - Prob. 5PCh. 2.7 - Prob. 6PCh. 2.7 - Prob. 7PCh. 2.7 - Prob. 8PCh. 2.7 - Prob. 9PCh. 2.7 - Prob. 10PCh. 2.7 - Prob. 11PCh. 2.7 - Prob. 12PCh. 2.7 - Prob. 14PCh. 2.7 - Prob. 15PCh. 2.7 - Prob. 16PCh. 2.7 - Prob. 17PCh. 2.8 - Prob. 1PCh. 2.8 - Prob. 2PCh. 2.8 - Prob. 3PCh. 2.8 - Prob. 4PCh. 2.8 - Prob. 5PCh. 2.8 - Prob. 6PCh. 2.8 - Prob. 7PCh. 2.8 - Prob. 8PCh. 2.8 - Prob. 9PCh. 2.8 - Prob. 10PCh. 2.8 - Prob. 11PCh. 2.8 - Prob. 12PCh. 2.8 - Prob. 13PCh. 2.8 - Prob. 14PCh. 2.8 - Prob. 15PCh. 2.8 - Prob. 16PCh. 2.8 - Prob. 17PCh. 2.8 - Prob. 18PCh. 2.9 - Prob. 1PCh. 2.9 - Prob. 2PCh. 2.9 - Prob. 3PCh. 2.9 - Prob. 4PCh. 2.9 - Prob. 5PCh. 2.9 - Prob. 6PCh. 2.9 - Prob. 7PCh. 2.9 - Prob. 8PCh. 2.9 - Prob. 9PCh. 2.9 - Prob. 10PCh. 2 - Prob. 1MPCh. 2 - Prob. 2MPCh. 2 - Prob. 3MPCh. 2 - Prob. 4MPCh. 2 - Prob. 5MPCh. 2 - Prob. 6MPCh. 2 - Prob. 7MPCh. 2 - Prob. 8MPCh. 2 - Prob. 9MPCh. 2 - Prob. 10MPCh. 2 - Prob. 11MPCh. 2 - Prob. 12MPCh. 2 - Prob. 13MPCh. 2 - Prob. 14MPCh. 2 - Prob. 15MPCh. 2 - Prob. 16MPCh. 2 - Prob. 17MPCh. 2 - Prob. 18MPCh. 2 - Prob. 19MPCh. 2 - Prob. 20MPCh. 2 - Prob. 21MPCh. 2 - Prob. 22MPCh. 2 - Prob. 23MPCh. 2 - Prob. 24MPCh. 2 - Prob. 25MPCh. 2 - Prob. 28MPCh. 2 - Prob. 29MPCh. 2 - Prob. 31MPCh. 2 - Prob. 32MPCh. 2 - Prob. 33MPCh. 2 - Prob. 34MPCh. 2 - Prob. 35MPCh. 2 - Prob. 36MPCh. 2 - Prob. 37MP
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