Differential Equations and Linear Algebra (4th Edition)
Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Differential Equations
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Chapter 11.2, Problem 10P

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For Problems 9-12, determine two linearly independent power series solutions to the given differential equation centered at x = 0 . Give a lower bound on the radius of convergence of the series solutions obtained.

( 1 + x 2 ) y ″ + 4 x y ′ + 2 y = 0 .

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Chapter 11 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 11.1 - True-False Review For Questions a-j, decide if the...Ch. 11.1 - Prob. 2TFRCh. 11.1 - Prob. 3TFRCh. 11.1 - Prob. 4TFRCh. 11.1 - Prob. 5TFRCh. 11.1 - True-False Review For Questions a-j, decide if the...Ch. 11.1 - Prob. 7TFRCh. 11.1 - Prob. 8TFRCh. 11.1 - Prob. 9TFRCh. 11.1 - Prob. 10TFR
Ch. 11.1 - Problems For Problems 1-6, determine the radius of...Ch. 11.1 - For Problems 1-6, determine the radius of...Ch. 11.1 - Problems For Problems 1-6, determine the radius of...Ch. 11.1 - Prob. 4PCh. 11.1 - Problems For Problems 1-6, determine the radius of...Ch. 11.1 - Problems For Problems 1-6, determine the radius of...Ch. 11.1 - Problems For problems 7-11, determine the radius...Ch. 11.1 - Problems For problems 7-11, determine the radius...Ch. 11.1 - Problems For problems 7-11, determine the radius...Ch. 11.1 - Problems For problems 7-11, determine the radius...Ch. 11.1 - Problems For problems 7-11, determine the radius...Ch. 11.1 - Problems a Determine all values of x at which the...Ch. 11.1 - Prob. 13PCh. 11.1 - Problems If f(x)=n=0anxn, where the coefficients...Ch. 11.1 - Problems Suppose it is known that the coefficients...Ch. 11.1 - Prob. 16PCh. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - Prob. 6TFRCh. 11.2 - Prob. 7TFRCh. 11.2 - Prob. 8TFRCh. 11.2 - Prob. 9TFRCh. 11.2 - True-False Review For Questions a-j, decide if the...Ch. 11.2 - Problems For Problems 18, determine two linear...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - For Problems 1-8, determine two linearly...Ch. 11.2 - Problems For Problems 912, determine two linearly...Ch. 11.2 - Problems For Problems 9-12, determine two linearly...Ch. 11.2 - For Problems 912, determine two linearly...Ch. 11.2 - Problems For Problems 9-12, determine two linearly...Ch. 11.2 - For Problems 1316, determine terms up to and...Ch. 11.2 - For Problems 1316, determine terms up to and...Ch. 11.2 - For Problems 1316, determine terms up to and...Ch. 11.2 - For Problems 1316, determine terms up to and...Ch. 11.2 - Consider the differential equation...Ch. 11.2 - Determine a series solution to the initial-value...Ch. 11.2 - Prob. 19PCh. 11.2 - Prob. 20PCh. 11.2 - Prob. 21PCh. 11.3 - Prob. 2PCh. 11.3 - Prob. 3PCh. 11.3 - Prob. 4PCh. 11.3 - Prob. 5PCh. 11.3 - Prob. 6PCh. 11.3 - Prob. 7PCh. 11.3 - Problems 8-10 deal with Hermites equation:...Ch. 11.3 - Problems Problems 8-10 deal with Hermites...Ch. 11.3 - When suitably normalized, the polynomial solutions...Ch. 11.3 - Prob. 11PCh. 11.3 - For Problems 1213, use some form of technology to...Ch. 11.4 - Problems For Problems 1-5, determine all singular...Ch. 11.4 - Problems For Problems 1-5, determine all singular...Ch. 11.4 - Prob. 3PCh. 11.4 - Prob. 4PCh. 11.4 - Prob. 5PCh. 11.4 - Prob. 6PCh. 11.4 - Prob. 7PCh. 11.4 - Problems For Problems 6-9, determine the roots of...Ch. 11.4 - Prob. 9PCh. 11.4 - Problems For Problems 10-17, show that the...Ch. 11.4 - Prob. 11PCh. 11.4 - Problems For Problems 10-17, show that the...Ch. 11.4 - Problems For Problems 10-17, show that the...Ch. 11.4 - For Problems 10-17, show that the indicial...Ch. 11.4 - Problems For Problems 10-17, show that the...Ch. 11.4 - Problems For Problems 10-17, show that the...Ch. 11.4 - Prob. 17PCh. 11.4 - Prob. 18PCh. 11.4 - Prob. 19PCh. 11.5 - True-False Review For Questions a-f, decide if the...Ch. 11.5 - Prob. 2TFRCh. 11.5 - Prob. 3TFRCh. 11.5 - Prob. 4TFRCh. 11.5 - Prob. 5TFRCh. 11.5 - Prob. 6TFRCh. 11.5 - For Problem 18, determine the roots of the...Ch. 11.5 - Prob. 2PCh. 11.5 - Prob. 3PCh. 11.5 - For Problem 18, determine the roots of the...Ch. 11.5 - Prob. 5PCh. 11.5 - Prob. 6PCh. 11.5 - Prob. 7PCh. 11.5 - For Problem 18, determine the roots of the...Ch. 11.5 - Prob. 9PCh. 11.5 - Prob. 10PCh. 11.5 - Show that x2(1+x)y"+x2y2y=0 has two linearly...Ch. 11.5 - For Problem 1427, determine two linearly...Ch. 11.5 - For Problem 1427, determine two linearly...Ch. 11.5 - For Problem 1427, determine two linearly...Ch. 11.5 - For Problem 1427, determine two linearly...Ch. 11.5 - For Problem 1427, determine two linearly...Ch. 11.5 - Prob. 19PCh. 11.5 - Prob. 20PCh. 11.5 - Prob. 22PCh. 11.5 - Prob. 23PCh. 11.5 - Prob. 24PCh. 11.5 - Prob. 25PCh. 11.5 - Prob. 27PCh. 11.5 - For Problems 28-29, determine a Frobenius series...Ch. 11.5 - For Problems 28-29, determine a Frobenius series...Ch. 11.6 - Problems Use the relations (11.6.4) and (11.6.5)...Ch. 11.6 - Problems Determine two linearly independent...Ch. 11.6 - Problems Let (p) denote the gamma function. Show...Ch. 11.6 - Prob. 5PCh. 11.6 - aBy making the change of variable t=x2 in the...Ch. 11.6 - aGiven that (1/2)= by Problem 6, determine (3/2)...Ch. 11.6 - Let Jp(x) denote the Bessel function of the first...Ch. 11.6 - Prob. 9PCh. 11.6 - Prob. 10PCh. 11.6 - Prob. 11PCh. 11.6 - Show that a J0(x)=J0(x)x1J0(x). b...Ch. 11.6 - Prob. 13PCh. 11.6 - Prob. 14PCh. 11.6 - Show that a J2(x)=J0(x)+2J0(x). b...Ch. 11.6 - Prob. 17PCh. 11.6 - Determine the Fourier-Bessel expansion in the...Ch. 11.6 - Prob. 19PCh. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - Prob. 4APCh. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - Prob. 6APCh. 11.7 - Additional Problems For Problems 113 determine...Ch. 11.7 - Additional Problems For Problems 113 determine...Ch. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - Prob. 10APCh. 11.7 - For Problems 113 determine whether x=0 is an...Ch. 11.7 - For problems 1-13, determine whether x=0 is a...Ch. 11.7 - Prob. 13APCh. 11.7 - Consider the hypergeometric equation...Ch. 11.7 - Consider the differential equation...Ch. 11.7 - Prob. 16APCh. 11.7 - Consider the differential equation...Ch. 11.7 - Prob. 18APCh. 11.7 - Prob. 19AP

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