1. Find the general solution of these constant coefficient linear inhomoge- neous ODEs, using the method of undetermined coefficients. (Note: you will need to find both the general solution to the homogeneous problem, and also a particular solution to the inhomogeneous problem.) (a) y" + 3y' + 2y = 6x — 1. (b) y"+y=x²eª. (c) y"-y-y=sin(x). (d) y" + y = 2x sin(x).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(d) please. I got to the point where i tried to find yp. I tried to use yp(x) = x(Asin(2x)+Bcos(2x)) but when inserting it into ODE I get A = 0 and B = 0 which can't be correct. Thank you for your help!!

 

1. Find the general solution of these constant coefficient linear inhomoge-
neous ODEs, using the method of undetermined coefficients.
(Note: you will need to find both the general solution to the
homogeneous problem, and also a particular solution to the
inhomogeneous problem.)
(a) y" + 3y' + 2y = 6x - 1.
(b) y" + y = x²ex.
(c) y" — y' - y = sin(x).
(d) y"+y= 2x sin(x).
Transcribed Image Text:1. Find the general solution of these constant coefficient linear inhomoge- neous ODEs, using the method of undetermined coefficients. (Note: you will need to find both the general solution to the homogeneous problem, and also a particular solution to the inhomogeneous problem.) (a) y" + 3y' + 2y = 6x - 1. (b) y" + y = x²ex. (c) y" — y' - y = sin(x). (d) y"+y= 2x sin(x).
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