This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the ta below, at left are various right sides f(z), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that yp, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = az² Yp = ax² + bx, Bƒ=1², c_f=1², Yp = az² + bx + c
This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the ta below, at left are various right sides f(z), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that yp, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = az² Yp = ax² + bx, Bƒ=1², c_f=1², Yp = az² + bx + c
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:This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the table
below, at left are various right sides f(x), and across from that at right is a form of a particular solution yp. For each line determine the
constants from a, b, c such that y, is a solution, or state that the given form is not a solution for any such values.
A f = x²,
Yp = ax²
B f = x²,
Ур
= ax² + bx,
c f = x²,
f = x²+3x+1,
Yp = ax² + bx + c
D
Yp = ax² + bx + c,
E f = e¹,
4x
Yp = ae
F
f = e³,
Yp = ae
Gf=e³,
H_f = e²,
| f = e²,
J f = e²
Ур = axe
2x
ae²z
Yp = ae
Yp = axe²
Ур
=
az²e²x
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