11. Consider the ODE y (8) - 2y (6) - 7y(4) – 4y" : = x 2 cos x + 3 sinx. The auxiliary equation for this ODE factors as 8-276-74-4r² = r² (r² + 1)² (r + 2)(r - 2). When using the method of undetermined coefficients to solve this equation, what would be your guess for the form of yp? Label the undetermined coefficients as A, B, etc. You do not need to find the numerical value of these coefficients. = Yp Ax² + Bx³ + Cr² sin x + Dx² cos x
11. Consider the ODE y (8) - 2y (6) - 7y(4) – 4y" : = x 2 cos x + 3 sinx. The auxiliary equation for this ODE factors as 8-276-74-4r² = r² (r² + 1)² (r + 2)(r - 2). When using the method of undetermined coefficients to solve this equation, what would be your guess for the form of yp? Label the undetermined coefficients as A, B, etc. You do not need to find the numerical value of these coefficients. = Yp Ax² + Bx³ + Cr² sin x + Dx² cos x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:11.
Consider the ODE
The auxiliary equation for this ODE factors as
Yp
y (8) - 2y (6) 7y(4) - 4y" = x-2 cos x + 3 sinx.
p8-276-74-4r² = r² (r.² + 1)² (r + 2)(r − 2).
When using the method of undetermined coefficients to solve this equation, what would be your
guess for the form of yp? Label the undetermined coefficients as A, B, etc. You do not need to find
the numerical value of these coefficients.
=
Ax² + Bx³ + Cr² sin x + Dx² cos x
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