Elementary Differential Equations
10th Edition
ISBN: 9780470458327
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley, John & Sons, Incorporated
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Chapter 7.1, Problem 19P
(a)
To determine
To show: The difference between the voltage drops of the circuit
(b)
To determine
To show: The sum of the currents of the circuit
(c)
To determine
To derive: The equations
(c)
To determine
To show: The equations
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Calculs Insights
πT
| cos x |³ dx
59
2
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
True or False and why
Chapter 7 Solutions
Elementary Differential Equations
Ch. 7.1 - In each of Problems 1 through 4, transform the...Ch. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - In each of Problems 1 through 4, transform the...Ch. 7.1 - Prob. 5PCh. 7.1 - In each of Problems 5 and 6, transform the given...Ch. 7.1 - Systems of first order equations can sometimes be...Ch. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - In each of Problems 8 through 12, proceed as in...
Ch. 7.1 - Prob. 11PCh. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.1 - Consider the circuit shown in Figure 7.1.2. Let...Ch. 7.1 - Prob. 20PCh. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.2 - Prob. 24PCh. 7.2 - Prob. 25PCh. 7.2 - Prob. 26PCh. 7.3 - In each of Problems 1 through 6, either solve the...Ch. 7.3 - In each of Problems 1 through 6, either solve the...Ch. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 31PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.4 - Prove the generalization of Theorem 7.4.1, as...Ch. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.5 - In each of Problems 1 through 6:
Find the general...Ch. 7.5 - Prob. 2PCh. 7.5 - Prob. 3PCh. 7.5 - In each of Problems 1 through 6:
Find the general...Ch. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10PCh. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - In each of Problems 9 through 14, find the general...Ch. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - Prob. 17PCh. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - Prob. 20PCh. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.5 - Prob. 28PCh. 7.5 - Prob. 29PCh. 7.5 - Prob. 30PCh. 7.5 - Prob. 31PCh. 7.5 - Prob. 32PCh. 7.5 - Prob. 33PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 2PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 4PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 7PCh. 7.6 - Prob. 8PCh. 7.6 - In each of Problems 9 and 10, find the solution of...Ch. 7.6 - Prob. 10PCh. 7.6 - Prob. 11PCh. 7.6 - Prob. 12PCh. 7.6 - Prob. 13PCh. 7.6 - Prob. 14PCh. 7.6 - Prob. 15PCh. 7.6 - Prob. 16PCh. 7.6 - Prob. 17PCh. 7.6 - Prob. 18PCh. 7.6 - Prob. 19PCh. 7.6 - Prob. 20PCh. 7.6 - Prob. 21PCh. 7.6 - Prob. 22PCh. 7.6 - Prob. 23PCh. 7.6 - Prob. 24PCh. 7.6 - Prob. 25PCh. 7.6 - Prob. 26PCh. 7.6 - Prob. 27PCh. 7.6 - Prob. 28PCh. 7.6 - Prob. 29PCh. 7.7 - In each of Problems 1 through 10:
Find a...Ch. 7.7 - Prob. 2PCh. 7.7 - Prob. 3PCh. 7.7 - Prob. 4PCh. 7.7 - Prob. 5PCh. 7.7 - Prob. 6PCh. 7.7 - Prob. 7PCh. 7.7 - Prob. 8PCh. 7.7 - Prob. 9PCh. 7.7 - Prob. 10PCh. 7.7 - Prob. 11PCh. 7.7 - Prob. 12PCh. 7.7 - Prob. 13PCh. 7.7 - Prob. 14PCh. 7.7 - Prob. 15PCh. 7.7 - Prob. 16PCh. 7.7 - Prob. 17PCh. 7.7 - Prob. 18PCh. 7.8 - Prob. 1PCh. 7.8 - Prob. 2PCh. 7.8 - Prob. 3PCh. 7.8 - Prob. 4PCh. 7.8 - Prob. 5PCh. 7.8 - Prob. 6PCh. 7.8 - Prob. 7PCh. 7.8 - Prob. 8PCh. 7.8 - Prob. 9PCh. 7.8 - Prob. 10PCh. 7.8 - Prob. 13PCh. 7.8 - Prob. 14PCh. 7.8 - Prob. 15PCh. 7.8 - Prob. 16PCh. 7.8 - Prob. 17PCh. 7.8 - Prob. 18PCh. 7.8 - Prob. 19PCh. 7.8 - Prob. 20PCh. 7.8 - Prob. 21PCh. 7.8 - Prob. 22PCh. 7.9 - Prob. 1PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 3PCh. 7.9 - Prob. 4PCh. 7.9 - Prob. 5PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 7PCh. 7.9 - Prob. 8PCh. 7.9 - Prob. 9PCh. 7.9 - Prob. 10PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 12PCh. 7.9 - Prob. 13PCh. 7.9 - Prob. 14PCh. 7.9 - Prob. 15PCh. 7.9 - Prob. 16PCh. 7.9 - Prob. 17PCh. 7.9 - Prob. 18P
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