
Calculus Volume 3
16th Edition
ISBN: 9781938168079
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Textbook Question
Chapter 7.4, Problem 113E
Find a power series solution for the following differential equations.
113.
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Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)
Q1:
A slider in a machine moves along a fixed straight rod. Its
distance x cm along the rod is given below for various values of the time. Find the
velocity and acceleration of the slider when t = 0.3 seconds.
t(seconds)
x(cm)
0 0.1 0.2 0.3 0.4 0.5 0.6
30.13 31.62 32.87 33.64 33.95 33.81 33.24
Q2:
Using the Runge-Kutta method of fourth order, solve for y atr = 1.2,
From
dy_2xy +et
=
dx x²+xc*
Take h=0.2.
given x = 1, y = 0
Q3:Approximate the solution of the following equation
using finite difference method.
ly -(1-y=
y = x), y(1) = 2 and y(3) = −1
On the interval (1≤x≤3).(taking h=0.5).
Ф
sketch stability
x= -4x + 2xy - 8
y° =
4 y 2 - x²
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Chapter 7 Solutions
Calculus Volume 3
Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - Classify each of the following equations as linear...Ch. 7.1 - For each of the following problems, verify that...Ch. 7.1 - For each of the following problems, verify that...Ch. 7.1 - For each of the following problems, verify that...Ch. 7.1 - For each of the following problems, verify that...
Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Find the general solution to the linear...Ch. 7.1 - Solve the initial-value problem. 31. y+5y+6y=0 , ...Ch. 7.1 - Solve the initial-value problem. 32. y+2y8y=0 , ...Ch. 7.1 - Solve the initial-value problem. 33. y+4y=0 , ...Ch. 7.1 - Solve the initial-value problem. 34. y18y+81y=0 , ...Ch. 7.1 - Solve the initial-value problem. 35. yy30y=0 , ...Ch. 7.1 - Solve the initial-value problem. 36. 4y+4y8y=0 , ...Ch. 7.1 - Solve the initial-value problem. 37. 25y+10y+y=0 ,...Ch. 7.1 - Solve the initial-value problem. 38. y+y=0 , ...Ch. 7.1 - Solve the boundary-value problem, if possible. 39....Ch. 7.1 - Solve the boundary-value problem, if possible. 40....Ch. 7.1 - Solve the boundary-value problem, if possible. 41....Ch. 7.1 - Solve the boundary-value problem, if possible. 42....Ch. 7.1 - Solve the boundary-value problem, if possible. 43....Ch. 7.1 - Solve the boundary-value problem, if possible. 44....Ch. 7.1 - Solve the boundary-value problem, if possible. 45....Ch. 7.1 - Solve the boundary-value problem, if possible. 46....Ch. 7.1 - Find a differential equation with a general...Ch. 7.1 - Find a differential equation with a general...Ch. 7.1 - For each of the following differential equations:...Ch. 7.1 - For each of the following differential equations:...Ch. 7.1 - For each of the following differential equations:...Ch. 7.1 - (Principle of superposition) Prove that if y1(x)...Ch. 7.1 - Prove that if a, b, and c are positive constants,...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - Solve the following equations using the method of...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - In each of the following problems, a. Write the...Ch. 7.2 - Solve the differential equation using either the...Ch. 7.2 - Solve the differential equation using either the...Ch. 7.2 - Solve the differential equation using either the...Ch. 7.2 - Solve the differential equation using either the...Ch. 7.2 - Solve the differential equation using the method...Ch. 7.2 - Solve the differential equation using the method...Ch. 7.2 - Solve the differential equation using the method...Ch. 7.2 - Solve the differential equation using the method...Ch. 7.2 - Find the unique solution satisfying the...Ch. 7.2 - Find the unique solution satisfying the...Ch. 7.2 - Find the unique solution satisfying the...Ch. 7.2 - Find the unique solution satisfying the...Ch. 7.2 - In each of the following problems, two linearly...Ch. 7.2 - In each of the following problems, two linearly...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Landing Vehicle NASA is planning a mission to...Ch. 7.3 - Resonance Consider an undamped system exhibiting...Ch. 7.3 - Resonance Consider an undamped system exhibiting...Ch. 7.3 - Resonance Consider an undamped system exhibiting...Ch. 7.3 - Resonance Consider an undamped system exhibiting...Ch. 7.3 - Resonance Consider an undamped system exhibiting...Ch. 7.3 - A mass weighing 4 lb stretches a spring 8 in. Find...Ch. 7.3 - A mass weighing 2 lb stretches a spring 2 ft. Find...Ch. 7.3 - A 100-g mass stretches a spring 0.1 m. Find the...Ch. 7.3 - A 400-g mass swatches a spring 5 cm. Find the...Ch. 7.3 - A block has a mass of 9 kg and is attached to a...Ch. 7.3 - A block has a mass of 5 kg and is attached to a...Ch. 7.3 - A 1-kg mass is attached to a vertical spring with...Ch. 7.3 - An 800-lb weight (25 slugs) is attached to a...Ch. 7.3 - A 9-kg mass is attached to a vertical spring with...Ch. 7.3 - A l-kg mass stretches a spring 6.25 cm. The...Ch. 7.3 - A 32-lb weight (1 slug) stretches a vertical...Ch. 7.3 - A 64-lb weight is attached to a vertical spring...Ch. 7.3 - A mass that weighs 8 lb stretches a spring 6...Ch. 7.3 - A mass that weighs 6 lb stretches a spring 3 in....Ch. 7.3 - Find the charge on the capacitor in an RLC series...Ch. 7.3 - Find the charge on the capacitor in an RLC series...Ch. 7.3 - A series circuit consists of a device where L=1H ,...Ch. 7.3 - A series circuit consists of a device where L=12H...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7.4 - Find a power series solution for the following...Ch. 7 - True or False? Justify your answer with a proof or...Ch. 7 - True or False? Justify your answer with a proof or...Ch. 7 - True or False? Justify your answer with a proof or...Ch. 7 - True or False? Justify your answer with a proof or...Ch. 7 - Classify the differential equation. Determine the...Ch. 7 - Classify the differential equation. Determine the...Ch. 7 - Classify the differential equation. Determine the...Ch. 7 - Classify the differential equation. Determine the...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the general...Ch. 7 - For the following problems, find the solution to...Ch. 7 - For the following problems, find the solution to...Ch. 7 - For the following problems, find the solution to...Ch. 7 - For the following problems, find the solution to...Ch. 7 - For the following problem, set up and solve the...Ch. 7 - The following problems consider the “beats” that...Ch. 7 - The following problems consider the “beats” that...Ch. 7 - The following problems consider the “beats” that...Ch. 7 - For the following problem, set up and solve the...
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