Given the differential equation y" - 8 y' + 16y 7sin(9x)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given the differential equation
y" - 8 y' + 16y
7sin(9x)
And the Solutions to its Characteristic Equation
Characteristic Solutions: R, = 4 and R, = 4
%3D
(1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the
Differential Equation.
A
y, = [Ax + B] cos(9x) + [Cx + D] sin(9x)
B.
y, = [Ax + B]e cos(9x) + [Cx + D]et sin(9x)
yp
= A e cos(9x) + Be" sin(9x)
e* sin(9x)
D
Ур
= A cos(9x) + B sin(9x)
E
= A sin( 9x)
F
y, = A e* sin(9x)
Transcribed Image Text:Given the differential equation y" - 8 y' + 16y 7sin(9x) And the Solutions to its Characteristic Equation Characteristic Solutions: R, = 4 and R, = 4 %3D (1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the Differential Equation. A y, = [Ax + B] cos(9x) + [Cx + D] sin(9x) B. y, = [Ax + B]e cos(9x) + [Cx + D]et sin(9x) yp = A e cos(9x) + Be" sin(9x) e* sin(9x) D Ур = A cos(9x) + B sin(9x) E = A sin( 9x) F y, = A e* sin(9x)
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