[19] Consider (*) y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).
[19] Consider (*) y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
My particular form solution looks like At^2+Bt+C+Dsin(4t)+Ecos(4t)+Fe^(2t), I know this is correct.
I keep getting sin(4t)*(-16D-16E+4D)+cos(4t)*9-16E+16D+4E) which reduces to sin(4t)*(-12D-16E)+cos(4t)*9-12E+16D) which gets me D=(-4/3)E and E=-47/18 which is wrong, I even plugged it into an online diffeq solver which shows D=2/5 and E=-3/10 respectively. So I know there's something wrong with my application of method of undetermined coefficients.
Transcribed Image Text:Enter an equation (and, optionally, the initial conditions):
y"+4y'+4y=8t^2+10cos(4t)+8e^(2t)
For example, y"(x)+25y(x)=0, y(0)=1, y'(0)=2.
dy
dx
d²y
Write y' (2) instead of y" (x) instead of etc.
dx²
If the calculator did not compute something or you have identified an error, or you have a
suggestion/feedback, please write it in the comments below.
CALCULATE
Your input: solve 4y(t) + 4y' (t) + y″ (t) = 8t² + 8e²t + 10 cos (4t)
ANSWER
2 sin (4t)
5
e2t
y(t) = 2t²4t+ (C₁ + С₂t) e¯ + +
2
3 cos (4t)
10
+3
![[19] Consider (*) y" +4y' + 4y = 8t² + 10 cos(4t) + 8e²¹.
(a) Find the complementary solutions ye(t) of (*).
(b) If one uses the method of undetermined coefficients to find a particular solution y(t)
of (*), what is the suitable form of the trial solution y(t)?
(c) Find a particular solution y(t) of (*).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c89c353-252e-4eca-b673-064be33ffdb0%2Fc754380c-eb81-450c-b82a-c3b93d889622%2Fjbw2aro_processed.png&w=3840&q=75)
Transcribed Image Text:[19] Consider (*) y" +4y' + 4y = 8t² + 10 cos(4t) + 8e²¹.
(a) Find the complementary solutions ye(t) of (*).
(b) If one uses the method of undetermined coefficients to find a particular solution y(t)
of (*), what is the suitable form of the trial solution y(t)?
(c) Find a particular solution y(t) of (*).
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