Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 8.8, Problem 29E
To determine
The first five Legendre polynomials.
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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
чуг.
Chapter 8 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 8.1 - In Problems 18, determine the first three nonzero...Ch. 8.1 - In Problems 18, determine the first three nonzero...Ch. 8.1 - In Problems 18, determine the first three nonzero...Ch. 8.1 - In Problems 18, determine the first three nonzero...Ch. 8.1 - In Problems 18, determine the first three nonzero...Ch. 8.1 - In Problems 1-8, determine the first three nonzero...Ch. 8.1 - In Problems 1-8, determine the first three nonzero...Ch. 8.1 - In Problems 1-8, determine the first three nonzero...Ch. 8.1 - a. Construct the Taylor polynomial p3(x) of degree...Ch. 8.1 - a. Construct the Taylor polynomial p3(x) of degree...
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Duffings Equation. In the study of a nonlinear...Ch. 8.1 - Soft versus Hard Springs. For Duffings equation...Ch. 8.1 - Prob. 15ECh. 8.1 - van der Pol Equation. In the study of the vacuum...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - In Problems 1-6, determine the convergence set of...Ch. 8.2 - Prob. 7ECh. 8.2 - Determine the convergence set of the given power...Ch. 8.2 - In Problems 9 and 10, find the power series...Ch. 8.2 - In Problems 9 and 10, find the power series...Ch. 8.2 - In Problems 11-14, find the first three nonzero...Ch. 8.2 - In Problems 11-14, find the first three nonzero...Ch. 8.2 - Prob. 13ECh. 8.2 - In Problems 11-14, find the first three nonzero...Ch. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - In Problems 17-20, find a power series expansion...Ch. 8.2 - Prob. 19ECh. 8.2 - In Problems 17-20, find a power series expansion...Ch. 8.2 - Prob. 21ECh. 8.2 - In Problems 21 and 22, find a power series...Ch. 8.2 - Prob. 23ECh. 8.2 - In Problems 23-26, express the given power series...Ch. 8.2 - Prob. 25ECh. 8.2 - In Problems 23-26, express the given power series...Ch. 8.2 - Prob. 27ECh. 8.2 - Show that...Ch. 8.2 - In Problems 29-34, determine the Taylor series...Ch. 8.2 - In Problems 2934, determine the Taylor series...Ch. 8.2 - Prob. 31ECh. 8.2 - In Problems 2934, determine the Taylor series...Ch. 8.2 - Prob. 33ECh. 8.2 - In Problems 2934, determine the Taylor series...Ch. 8.2 - Prob. 35ECh. 8.2 - Let f(x) and g(x) be analytic at x0. Determine...Ch. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - Prob. 4ECh. 8.3 - In Problem 110, determine all the singular points...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - In Problems 110, determine all the singular points...Ch. 8.3 - In Problems 1118, find at least the first four...Ch. 8.3 - In Problems 1118, find at least the first four...Ch. 8.3 - Prob. 13ECh. 8.3 - In Problems 1118, find at least the first four...Ch. 8.3 - In Problems 1118, find at least the first four...Ch. 8.3 - Prob. 16ECh. 8.3 - In Problems 1118, find at least the first four...Ch. 8.3 - Prob. 18ECh. 8.3 - In Problems 1924, find a power series expansion...Ch. 8.3 - In Problems 1924, find a power series expansion...Ch. 8.3 - In Problems 1924, find a power series expansion...Ch. 8.3 - In Problems 1924, find a power series expansion...Ch. 8.3 - In Problems 1924, find a power series expansion...Ch. 8.3 - In Problems 19-24, find a power series expansion...Ch. 8.3 - In Problems 25-28, find at least the first four...Ch. 8.3 - Prob. 26ECh. 8.3 - In Problems 25-28, find at least the first four...Ch. 8.3 - In Problems 25-28, find at least the first four...Ch. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - In Problems 29-31, use the first few terms of the...Ch. 8.3 - Prob. 32ECh. 8.3 - Use the ratio test to show that the radius of...Ch. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Variable Spring Constant. As a spring is heated,...Ch. 8.4 - In Problems 16, find a minimum value for the...Ch. 8.4 - In Problems 16, find a minimum value for the...Ch. 8.4 - In Problems 16, find a minimum value for the...Ch. 8.4 - In Problems 16, find a minimum value for the...Ch. 8.4 - Prob. 5ECh. 8.4 - In Problems 16, find a minimum value for the...Ch. 8.4 - In Problems 712, find at least the first four...Ch. 8.4 - In Problems 712, find at least the first four...Ch. 8.4 - In Problems 712, find at least the first four...Ch. 8.4 - Prob. 10ECh. 8.4 - In Problems 712, find at least the first four...Ch. 8.4 - In Problems 712, find at least the first four...Ch. 8.4 - In Problems 1319, find at least the first four...Ch. 8.4 - In Problems 1319, find at least the first four...Ch. 8.4 - In Problems 1319, find at least the first four...Ch. 8.4 - Prob. 16ECh. 8.4 - In Problems 13-19, find at least the first four...Ch. 8.4 - In Problems 13-19, find at least the first four...Ch. 8.4 - In Problems 13-19, find at least the first four...Ch. 8.4 - To derive the general solution given by equations...Ch. 8.4 - In Problems 21-28, use the procedure illustrated...Ch. 8.4 - Prob. 22ECh. 8.4 - In Problems 21-28, use the procedure illustrated...Ch. 8.4 - Prob. 24ECh. 8.4 - In Problems 21-28, use the procedure illustrated...Ch. 8.4 - In Problems 21-28, use the procedure illustrated...Ch. 8.4 - In Problems 21-28, use the procedure illustrated...Ch. 8.4 - Prob. 28ECh. 8.4 - The equation (1x2)y2xy+n(n+1)y=0, where n is an...Ch. 8.4 - Aging Spring. As a spring ages, its spring...Ch. 8.4 - Aging Spring without Damping. In the mass-spring...Ch. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - In Problems 15-17, solve the given initial value...Ch. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.6 - In Problems 1-10, classify each singular point...Ch. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - In Problems 11-18, find the indicial equation and...Ch. 8.6 - In Problems 11-18, find the indicial equation and...Ch. 8.6 - In Problems 11-18, find the indicial equation and...Ch. 8.6 - In Problems 11-18, find the indicial equation and...Ch. 8.6 - In Problems 1118, find the indicial equation and...Ch. 8.6 - In Problems 1118, find the indicial equation and...Ch. 8.6 - In Problems 1118, find the indicial equation and...Ch. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - In Problems 39 and 40, try to use the method of...Ch. 8.6 - Prob. 40ECh. 8.6 - Prob. 41ECh. 8.6 - Prob. 42ECh. 8.6 - Prob. 43ECh. 8.6 - Prob. 44ECh. 8.6 - Prob. 45ECh. 8.6 - Prob. 46ECh. 8.6 - Prob. 47ECh. 8.7 - In Problems 1-14, find at least the first three...Ch. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - In Problems 1-14, find at least the first three...Ch. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - In Problems 1-14, find at least the first three...Ch. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - In Problems 15 and 16, determine whether the given...Ch. 8.7 - Prob. 16ECh. 8.7 - In Problems 17-20, find at least the first three...Ch. 8.7 - Prob. 18ECh. 8.7 - In Problems 17-20, find at least the first three...Ch. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - In Problem 21 consider a column with a rectangular...Ch. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - To obtain two linearly independent solutions to...Ch. 8.8 - In Problems 1-4, express a general solution to the...Ch. 8.8 - Prob. 2ECh. 8.8 - In Problems 1-4, express a general solution to the...Ch. 8.8 - In Problems 1-4, express a general solution to the...Ch. 8.8 - Prob. 5ECh. 8.8 - Prob. 6ECh. 8.8 - Prob. 7ECh. 8.8 - Prob. 8ECh. 8.8 - Prob. 9ECh. 8.8 - Prob. 10ECh. 8.8 - Show that the confluent hypergeometric equation...Ch. 8.8 - Prob. 12ECh. 8.8 - Prob. 13ECh. 8.8 - Prob. 14ECh. 8.8 - Prob. 15ECh. 8.8 - Prob. 16ECh. 8.8 - Prob. 17ECh. 8.8 - Prob. 18ECh. 8.8 - In Problems 19 and 20, a Bessel equation is given....Ch. 8.8 - Prob. 21ECh. 8.8 - Prob. 22ECh. 8.8 - Prob. 23ECh. 8.8 - Prob. 24ECh. 8.8 - Show that J1/2(x)=(2/x)1/2sinx and...Ch. 8.8 - The Bessel functions of order v=n+1/2, n any...Ch. 8.8 - Prob. 27ECh. 8.8 - Prob. 28ECh. 8.8 - Prob. 29ECh. 8.8 - Prob. 30ECh. 8.8 - Prob. 31ECh. 8.8 - To prove Rodriguess formula (52) for Legendre...Ch. 8.8 - Prob. 34ECh. 8.8 - Prob. 35ECh. 8.8 - Prob. 36ECh. 8.8 - The Hermite polynomials Hn(x) are polynomial...Ch. 8.8 - Prob. 38ECh. 8.8 - Prob. 39ECh. 8.8 - Reduction to Bessels Equation. The class of...Ch. 8.8 - a. Show that the substitution z(x)=xy(x) renders...Ch. 8.RP - Find the first four nonzero terms in the Taylor...Ch. 8.RP - Prob. 2RPCh. 8.RP - Find at least the first four nonzero terms in a...Ch. 8.RP - Prob. 4RPCh. 8.RP - Find at least the first four nonzero terms in a...Ch. 8.RP - Prob. 6RPCh. 8.RP - Use the method of Frobenius to find at least the...Ch. 8.RP - Find the indicial equation and its roots and state...Ch. 8.RP - Find at least the first three nonzero terms in the...
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