Elementary Differential Equations
10th Edition
ISBN: 9780470458327
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley, John & Sons, Incorporated
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Chapter 5.5, Problem 5P
(a)
To determine
To show: The given differential equation has a regular singular point at
(b)
To determine
The indicial equation, the recurrence relation and the roots of the indicial equation.
(c)
To determine
The series solution
(d)
To determine
The series solution for the smaller root if roots are unequal.
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Chapter 5 Solutions
Elementary Differential Equations
Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 1 through 8, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...
Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - In each of Problems 9 through 16, determine the...Ch. 5.1 - Given that , compute y′ and y″ and write out the...Ch. 5.1 - Prob. 18PCh. 5.1 - Prob. 19PCh. 5.1 - Prob. 20PCh. 5.1 - Prob. 21PCh. 5.1 - Prob. 22PCh. 5.1 - Prob. 23PCh. 5.1 - Prob. 24PCh. 5.1 - Prob. 25PCh. 5.1 - Prob. 26PCh. 5.1 - Prob. 27PCh. 5.1 - Prob. 28PCh. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - Prob. 3PCh. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - Prob. 9PCh. 5.2 - Prob. 10PCh. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 1 through 14:
Seek power...Ch. 5.2 - In each of Problems 15 through 18:
(a) Find the...Ch. 5.2 - Prob. 16PCh. 5.2 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - Prob. 19PCh. 5.2 - Prob. 20PCh. 5.2 - The Hermite Equation. The equation
y″ − 2xy′ + λy...Ch. 5.2 - Consider the initial value problem
Show that y =...Ch. 5.2 - Prob. 23PCh. 5.2 - Prob. 24PCh. 5.2 - Prob. 25PCh. 5.2 - Prob. 26PCh. 5.2 - Prob. 27PCh. 5.2 - Prob. 28PCh. 5.3 - In each of Problems 1 through 4, determine ϕ″(x0),...Ch. 5.3 - In each of Problems 1 through 4, determine ϕ″(x0),...Ch. 5.3 - In each of Problems 1 through 4, determine ϕ″(x0),...Ch. 5.3 - In each of Problems 1 through 4, determine ϕ″(x0),...Ch. 5.3 - In each of Problems 5 through 8, determine a lower...Ch. 5.3 - In each of Problems 5 through 8, determine a lower...Ch. 5.3 - In each of Problems 5 through 8, determine a lower...Ch. 5.3 - In each of Problems 5 through 8, determine a lower...Ch. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - For each of the differential equations in Problems...Ch. 5.3 - For each of the differential equations in Problems...Ch. 5.3 - For each of the differential equations in Problems...Ch. 5.3 - Prob. 14PCh. 5.3 - Prob. 15PCh. 5.3 - Prob. 16PCh. 5.3 - Prob. 17PCh. 5.3 - Prob. 18PCh. 5.3 - Prob. 19PCh. 5.3 - Prob. 20PCh. 5.3 - Prob. 21PCh. 5.3 - Prob. 22PCh. 5.3 - Prob. 23PCh. 5.3 - Prob. 24PCh. 5.3 - Prob. 25PCh. 5.3 - Prob. 26PCh. 5.3 - Prob. 27PCh. 5.3 - Prob. 28PCh. 5.3 - Prob. 29PCh. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - In each of Problems 1 through 12, determine the...Ch. 5.4 - Prob. 9PCh. 5.4 - Prob. 10PCh. 5.4 - Prob. 11PCh. 5.4 - Prob. 12PCh. 5.4 - Prob. 13PCh. 5.4 - Prob. 14PCh. 5.4 - Prob. 15PCh. 5.4 - Prob. 16PCh. 5.4 - Prob. 17PCh. 5.4 - Prob. 18PCh. 5.4 - Prob. 19PCh. 5.4 - Prob. 20PCh. 5.4 - Prob. 21PCh. 5.4 - Prob. 22PCh. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Prob. 25PCh. 5.4 - In each of Problems 17 through 34, find all...Ch. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Prob. 29PCh. 5.4 - Prob. 30PCh. 5.4 - Prob. 31PCh. 5.4 - Prob. 32PCh. 5.4 - Prob. 33PCh. 5.4 - Prob. 34PCh. 5.4 - Prob. 35PCh. 5.4 - Prob. 36PCh. 5.4 - Prob. 37PCh. 5.4 - Prob. 38PCh. 5.4 - Prob. 39PCh. 5.4 - Prob. 40PCh. 5.4 - Prob. 41PCh. 5.4 - Prob. 42PCh. 5.4 - Prob. 43PCh. 5.4 - Prob. 44PCh. 5.4 - Prob. 45PCh. 5.4 - Prob. 46PCh. 5.4 - Prob. 47PCh. 5.4 - Prob. 48PCh. 5.4 - Prob. 49PCh. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - Prob. 9PCh. 5.5 - In each of Problems 1 through 10:
Show that the...Ch. 5.5 - The Legendre equation of order α is
(1 − x2)y″ −...Ch. 5.5 - The Chebyshev equation is
(1 − x2)y″ − xy′ + α2y =...Ch. 5.5 - Prob. 13PCh. 5.5 - The Bessel equation of order zero is
x2y″ + xy′ +...Ch. 5.5 - Prob. 15PCh. 5.5 - Prob. 16PCh. 5.6 - In each of Problems 1 through 12:
Find all the...Ch. 5.6 - In each of Problems 1 through 12:
Find all the...Ch. 5.6 - In each of Problems 1 through 12:
Find all the...Ch. 5.6 - Prob. 4PCh. 5.6 - Prob. 5PCh. 5.6 - Prob. 6PCh. 5.6 - Prob. 7PCh. 5.6 - Prob. 8PCh. 5.6 - Prob. 9PCh. 5.6 - In each of Problems 1 through 12:
Find all the...Ch. 5.6 - In each of Problems 1 through 12:
Find all the...Ch. 5.6 - Prob. 12PCh. 5.6 - Prob. 13PCh. 5.6 - Prob. 14PCh. 5.6 - Prob. 15PCh. 5.6 - Prob. 16PCh. 5.6 - Prob. 18PCh. 5.6 - Consider the differential equation
where α and β...Ch. 5.6 - Prob. 21PCh. 5.7 - Prob. 1PCh. 5.7 - Prob. 2PCh. 5.7 - Prob. 3PCh. 5.7 - Prob. 4PCh. 5.7 - Prob. 5PCh. 5.7 - Prob. 6PCh. 5.7 - Prob. 7PCh. 5.7 - Prob. 8PCh. 5.7 - Prob. 9PCh. 5.7 - Prob. 10PCh. 5.7 - Prob. 11PCh. 5.7 - Prob. 12PCh. 5.7 - Prob. 13PCh. 5.7 - Prob. 14P
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