Differential Equations: An Introduction to Modern Methods and Applications
3rd Edition
ISBN: 9781118531778
Author: James R. Brannan, William E. Boyce
Publisher: WILEY
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Chapter 8.1, Problem 6P
In each of Problems 5 through 10, draw a direction field for the given differential equation and state whether you think that the solutions are converging or diverging.
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30. An individual who has automobile insurance from a certain company is randomly selected. Let Y be the num- ber of moving violations for which the individual was cited during the last 3 years. The pmf of Y isy | 1 2 4 8 16p(y) | .05 .10 .35 .40 .10
a.Compute E(Y).b. Suppose an individual with Y violations incurs a surcharge of $100Y^2. Calculate the expected amount of the surcharge.
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24. An insurance company offers its policyholders a num- ber of different premium payment options. For a ran- domly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows:
F(x)=0.00 : x < 10.30 : 1≤x<30.40 : 3≤ x < 40.45 : 4≤ x <60.60 : 6≤ x < 121.00 : 12≤ x
a. What is the pmf of X?b. Using just the cdf, compute P(3≤ X ≤6) and P(4≤ X).
Chapter 8 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 1 through 4: a) Find...Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 5 through 10 , draw a...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10 , draw a...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...
Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - Consider the initial value problem...Ch. 8.1 - Consider the initial value problem
Use Euler’s...Ch. 8.1 - Consider the initial value problem...Ch. 8.1 - Consider the initial value problem
Where is a...Ch. 8.1 - Consider the initial value problem y=y2t2,y(0)=,...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - Complete the calculations leading to the entries...Ch. 8.2 - Using three terms in the Taylor series given in...Ch. 8.2 - In each of Problems 15 and 16, estimate the local...Ch. 8.2 - In each of Problems 15 and 16, estimate the local...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - Consider the initial value problem y=cos5t,y(0)=1....Ch. 8.2 - Using a step size h=0.05 and the Euler method,...Ch. 8.2 - The following problem illustrates a danger that...Ch. 8.2 - The distributive law a(bc)=abac does not hold, in...Ch. 8.2 - In this section we stated that the global...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - Complete the calculation leading to the entries in...Ch. 8.3 - Confirm the results in Table 8.3.2 by executing...Ch. 8.3 - Consider the initial value problem y=t2+y2,y(0)=1....Ch. 8.3 - Consider the initial value problem
Draw a...Ch. 8.3 - In this problem, we establish that the local...Ch. 8.3 - Consider the improved Euler method for solving the...Ch. 8.3 - In each of Problems 19 and 20, use the actual...Ch. 8.3 - In each of Problems 19 and 20, use the actual...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - Consider the example problemwith the initial...Ch. 8.4 - Consider the initial value problem...Ch. 8.P1 - Assume that the shape of the dispensers are...Ch. 8.P1 - After viewing the results of her computer...Ch. 8.P2 - Show that Euler’s method applied to the...Ch. 8.P2 - Simulate five sample trajectories of Eq. (1) for...Ch. 8.P2 - Use the differential equation (4) to generate an...Ch. 8.P2 - Variance Reduction by Antithetic Variates. A...
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