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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
icon
Related questions
Question

q15

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)
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,