FIRST CRSE.IN DIFF.EQUAT..-ACCESS
11th Edition
ISBN: 9781337652469
Author: ZILL
Publisher: CENGAGE L
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Chapter 2.5, Problem 15E
In Problems 15–20 solve the given differential equation by using an appropriate substitution.
15.
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Month Number (Thousands)Dec 1991 65.60Jan 1992 71.60Feb 1992 78.80Mar 1992 111.60Apr 1992 107.60May 1992 115.20Jun 1992 117.80Jul 1992 106.20Aug 1992 109.90Sep 1992 106.00Oct 1992 111.80Nov 1992 84.50Dec 1992 78.60Jan 1993 70.50Feb 1993 74.60Mar 1993 95.50Apr 1993 117.80May 1993 120.90Jun 1993 128.50Jul 1993 115.30Aug 1993 121.80Sep 1993 118.50Oct 1993 123.30Nov 1993 102.30Dec 1993 98.70Jan 1994 76.20Feb 1994 83.50Mar 1994 134.30Apr 1994 137.60May 1994 148.80Jun 1994 136.40Jul 1994 127.80Aug 1994 139.80Sep 1994 130.10Oct 1994 130.60Nov 1994 113.40Dec 1994 98.50Jan 1995 84.50Feb 1995 81.60Mar 1995 103.80Apr 1995 116.90May 1995 130.50Jun 1995 123.40Jul 1995 129.10Aug 1995…
Chapter 2 Solutions
FIRST CRSE.IN DIFF.EQUAT..-ACCESS
Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...
Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 13 and 14 the given figure represents...Ch. 2.1 - In Problems 13 and 14 the given figure represents...Ch. 2.1 - In parts (a) and (b) sketch isoclines f(x, y) = c...Ch. 2.1 - (a) Consider the direction field of the...Ch. 2.1 - Consider the autonomous first-order differential...Ch. 2.1 - Consider the autonomous first-order differential...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - In Problems 21-28 find the critical points and...Ch. 2.1 - Prob. 28ECh. 2.1 - In Problems 29 and 30 consider the autonomous...Ch. 2.1 - In Problems 29 and 30 consider the autonomous...Ch. 2.1 - Consider the autonomous DE dy/dx = (2/)y sin y...Ch. 2.1 - A critical point c of an autonomous first-order DE...Ch. 2.1 - Suppose that y(x) is a nonconstant solution of the...Ch. 2.1 - Prob. 34ECh. 2.1 - Using the autonomous equation (2), discuss how it...Ch. 2.1 - Prob. 36ECh. 2.1 - Suppose the autonomous DE in (2) has no critical...Ch. 2.1 - Population Model The differential equation in...Ch. 2.1 - Population Model Another population model is given...Ch. 2.1 - Terminal Velocity In Section 1.3 we saw that the...Ch. 2.1 - Suppose the model in Problem 40 is modified so...Ch. 2.1 - Chemical reactions When certain kinds of chemicals...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 122 solve the given differential...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 2328 find an explicit solution of the...Ch. 2.2 - In Problems 29 and 30 proceed as in Example 5 and...Ch. 2.2 - In Problems 29 and 30 proceed as in Example 5 and...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - In Problems 3134 find an explicit solution of the...Ch. 2.2 - (a) Find a solution of the initial-value problem...Ch. 2.2 - Find a solution of xdydx=y2y that passes through...Ch. 2.2 - Find a singular solution of Problem 21. Of Problem...Ch. 2.2 - Show that an implicit solution of...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Often a radical change in the form of the solution...Ch. 2.2 - Every autonomous first-order equation dy/dx = f(y)...Ch. 2.2 - (a) The autonomous first-order differential...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - In Problems 4550 use a technique of integration or...Ch. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - In Problems 43 and 44 we saw that every autonomous...Ch. 2.2 - Prob. 54ECh. 2.2 - Find a function whose square plus the square of...Ch. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 1-24 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - Prob. 22ECh. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 124 find the general solution of the...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 2536 solve the given initial-value...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 3740 proceed as in Example 6 to solve...Ch. 2.3 - In Problems 41 and 42 proceed as in Example 6 to...Ch. 2.3 - In Problems 41 and 42 proceed as in Example 6 to...Ch. 2.3 - In Problems 43 and 44 proceed as in Example 7 and...Ch. 2.3 - Prob. 44ECh. 2.3 - In Problems 45 and 46 proceed as in Example 7 and...Ch. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Reread Example 4 and then find the general...Ch. 2.3 - Reread the discussion following Example 5....Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - In determining the integrating factor (3), we did...Ch. 2.3 - Prob. 56ECh. 2.3 - Radioactive Decay Series The following system of...Ch. 2.3 - Heart Pacemaker A heart pacemaker consists of a...Ch. 2.3 - Prob. 61ECh. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In Problems 120 determine whether the given...Ch. 2.4 - In problems 2126 slove the given initial-value...Ch. 2.4 - In Problem 2126 solve the given initial-value...Ch. 2.4 - In problems 2126 solve the given intial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 2126 solve the given initial-value...Ch. 2.4 - In Problems 27 and 28 find the value of k so that...Ch. 2.4 - In Problems 27 and 28 find the value of k so that...Ch. 2.4 - In Problems 29 and 30 verify that the given...Ch. 2.4 - In Problems 29 and 30 verify that the given...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 3136 solve the given differential...Ch. 2.4 - In Problems 37 and 38 solve the given...Ch. 2.4 - In Problems 37 and 38 solve the given...Ch. 2.4 - (a) Show that a one-parameter family of solutions...Ch. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Discuss how the functions M(x, y) and N(x, y) can...Ch. 2.4 - Differential equations are sometimes solved by...Ch. 2.4 - True or False: Every separable first-order...Ch. 2.4 - Falling Chain A portion of a uniform chain of...Ch. 2.5 - Each DE in Problems 114 is homogeneous. In...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1-10 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1-10 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 110 solve the given differential...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1114 solve the given initial-value...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 1520 solve the given differential...Ch. 2.5 - In Problems 21 and 22 solve the given...Ch. 2.5 - In Problems 21 and 22 solve the given...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - In Problems 2328 solve the given differential...Ch. 2.5 - dydx=cos(x+y), y(0) = /4Ch. 2.5 - In Problems 29 and 30 solve the given...Ch. 2.5 - Explain why it is always possible to express any...Ch. 2.5 - Put the homogeneous differential equation...Ch. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - The differential equation dy/dx = P(x) + Q(x)y +...Ch. 2.5 - Determine an appropriate substitution to solve...Ch. 2.5 - Falling Chain In Problem 45 in Exercises 2.4 we...Ch. 2.5 - Population Growth In the study of population...Ch. 2.6 - In Problems 1 and 2 use Eulers method to obtain a...Ch. 2.6 - In Problems 1 and 2 use Eulers method to obtain a...Ch. 2.6 - In Problems 3 and 4 use Eulers method to obtain a...Ch. 2.6 - In Problems 3 and 4 use Eulers method to obtain a...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2.6 - In Problems 510 use a numerical solver and Eulers...Ch. 2 - Answer Problems 112 without referring back to the...Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - In Problems 13 and 14 construct an autonomous...Ch. 2 - The number 0 is a critical point of the autonomous...Ch. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Classify each differential equation as separable,...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - Prob. 21RECh. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 1926 solve the given differential...Ch. 2 - In Problems 2730 express the solution of the given...Ch. 2 - In Problems 2730 express the solution of the given...Ch. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - In Problems 31 and 32 solve the given...Ch. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - (a) Without solving, explain why the initial-value...Ch. 2 - (a) Find an implicit solution of the initial-value...Ch. 2 - Prob. 37RECh. 2 - Use Eulers method with step size h = 0.1 to...
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