Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 7.3, Problem 29E
In Problems 21–30 use the Laplace transform to solve the given initial-value problem.
29. y″ − y′ = et cos t, y(0) = 0, y′(0) = 0
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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 PercentApr 1972 4.97May 1972 5.00Jun 1972 5.04Jul 1972 5.25Aug 1972 5.27Sep 1972 5.50Oct 1972 5.73Nov 1972 5.75Dec 1972 5.79Jan 1973 6.00Feb 1973 6.02Mar 1973 6.30Apr 1973 6.61May 1973 7.01Jun 1973 7.49Jul 1973 8.30Aug 1973 9.23Sep 1973 9.86Oct 1973 9.94Nov 1973 9.75Dec 1973 9.75Jan 1974 9.73Feb 1974 9.21Mar 1974 8.85Apr 1974 10.02May 1974 11.25Jun 1974 11.54Jul 1974 11.97Aug 1974 12.00Sep 1974 12.00Oct 1974 11.68Nov 1974 10.83Dec 1974 10.50Jan 1975 10.05Feb 1975 8.96Mar 1975 7.93Apr 1975 7.50May 1975 7.40Jun 1975 7.07Jul 1975 7.15Aug 1975 7.66Sep 1975 7.88Oct 1975 7.96Nov 1975 7.53Dec 1975 7.26Jan 1976 7.00Feb 1976 6.75Mar 1976 6.75Apr 1976 6.75May 1976…
Using FDF, BDF, and CDF, find the first derivative;
1. The distance x of a runner from a fixed point is measured (in meters) at an
interval of half a second. The data obtained is:
t
0
x
0
0.5
3.65
1.0
1.5
2.0
6.80
9.90
12.15
Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s
2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input
of 2 assuming a step size of 1. Calculate using Analytical Solution and
Absolute Relative Error:
=
True Value - Approximate Value|
x100
True Value
3. Given the data below where f(x)
sin (3x), estimate f(1.5) using Langrage
Interpolation.
x
1
1.3
1.6
1.9
2.2
f(x)
0.14
-0.69
-0.99
-0.55
0.31
4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given
by:
30
x =
Loo (2000ln
140000
140000
-
2100
9.8t) dt
Using the Trapezoidal Rule, n=2, find the distance covered.
5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the
results for n=4 and n=8
Can you check if my step is correct?
Chapter 7 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 118 use Definition 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - Prob. 24ECh. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 1936 use Theorem 7.1.1 to find f(t)....Ch. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - In Problems 3740 find f(t) by first using a...Ch. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - In Problems 4346 use Problems 41 and 42 and the...Ch. 7.1 - Prob. 46ECh. 7.1 - Suppose that if {f1(t)} = F1(s) for s c1 and that...Ch. 7.1 - Figure 7.1.4 suggests, but does not prove, that...Ch. 7.1 - Discussion Problems Use part (c) of Theorem 7.1.1...Ch. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Show that the function f(t)=1/t2 does not possess...Ch. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - In Problems 5558 use the given Laplace transform...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - Prob. 22ECh. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 130 use appropriate algebra and...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3134 find the given inverse Laplace...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - Prob. 42ECh. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - In Problems 3544 use the Laplace transform to...Ch. 7.2 - The inverse forms of the results in Problem 49 in...Ch. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Make up two functions f1 and f2 that have the same...Ch. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - Find either F(s) or f (t), as indicated. {e2t(t ...Ch. 7.3 - Find either F(s) or f (t), as indicated. {et sin...Ch. 7.3 - Find either F(s) or f (t), as indicated. {e2t cos...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - Prob. 12ECh. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - Prob. 15ECh. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 120 find either F(s) or f(t), as...Ch. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - Prob. 28ECh. 7.3 - In Problems 2130 use the Laplace transform to...Ch. 7.3 - Prob. 30ECh. 7.3 - In Problems 31 and 32 use the Laplace transform...Ch. 7.3 - In Problems 31 and 32 use the Laplace transform...Ch. 7.3 - Prob. 33ECh. 7.3 - Recall that the differential equation for the...Ch. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - In Problems 3748 find either F(s) or f(t), as...Ch. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - Prob. 56ECh. 7.3 - In Problems 5562 write each function in terms of...Ch. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - In Problems 6370 use the Laplace transform to...Ch. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Suppose a 32-pound weight stretches a spring 2...Ch. 7.3 - Prob. 72ECh. 7.3 - Prob. 73ECh. 7.3 - Prob. 74ECh. 7.3 - Prob. 75ECh. 7.3 - Prob. 76ECh. 7.3 - Prob. 77ECh. 7.3 - Prob. 78ECh. 7.3 - Prob. 79ECh. 7.3 - Prob. 80ECh. 7.3 - Discuss how you would fix up each of the following...Ch. 7.3 - Prob. 83ECh. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - Prob. 6ECh. 7.4 - In Problems 18 use Theorem 7.4.1 to evaluate the...Ch. 7.4 - Prob. 8ECh. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - Prob. 10ECh. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - Prob. 13ECh. 7.4 - In Problems 914 use the Laplace transform to solve...Ch. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - In some instances the Laplace transform can be...Ch. 7.4 - In some instances the Laplace transform can be...Ch. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - In Problems 1922 proceed as in Example 3 and find...Ch. 7.4 - Prob. 22ECh. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - Prob. 33ECh. 7.4 - In Problems 2334 proceed as in Example 4 and find...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - Prob. 46ECh. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - In Problems 4150 use the Laplace transform to...Ch. 7.4 - Prob. 50ECh. 7.4 - In Problems 51 and 52 solve equation (10) subject...Ch. 7.4 - Prob. 52ECh. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - In Problems 5358 use Theorem 7.4.3 to find the...Ch. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - (a)Laguerres differential equation ty+(1t)y+ny=0...Ch. 7.4 - Prob. 66ECh. 7.4 - Prob. 67ECh. 7.4 - Prob. 68ECh. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Appropriately modify the procedure of Problem 72...Ch. 7.4 - Prob. 74ECh. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - In Problems 112 use the Laplace transform to solve...Ch. 7.5 - Prob. 12ECh. 7.5 - In Problems 13 and 14 use the Laplace transform to...Ch. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - d2xdt2+xy=0d2ydt2+yx=0 x(0) = 0, x(0) = 2, y(0) =...Ch. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - dxdt4x+d3ydt3=6sintdxdt+2x2d3ydt3=0 x(0) = 0, y(0)...Ch. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - (a) Show that the system of differential equations...Ch. 7.6 - (a) In Problem 12 in Exercises 3.3 you were asked...Ch. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7 - In Problems 1 and 2 use the definition of the...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - In Problems 2932 express f in terms of unit step...Ch. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - A uniform cantilever beam of length L is embedded...Ch. 7 - When a uniform beam is supported by an elastic...Ch. 7 - Prob. 49RECh. 7 - Coulomb Friction Revlslted In Problem 27 in...Ch. 7 - Range of a ProjectileNo Air Resistance (a) A...
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