Need help finding A1 and A0. The question is: Find a particular solution to the differential equation, y'' - 5y' + 6y = tet. I am getting stuck at the bottom with the final part. I have included my work. Thank you for your time!
Need help finding A1 and A0. The question is: Find a particular solution to the differential equation, y'' - 5y' + 6y = tet. I am getting stuck at the bottom with the final part. I have included my work. Thank you for your time!
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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Need help finding A1 and A0. The question is: Find a particular solution to the
![4d) y "- 5y' + by = te ²
(1-2)(x-3) = 0
r₁ = 2
r₂ = 3
m=1
Yo (t) = ( A₁ t`'+ A₂) e +
= A₁ te ¹ + A₂e *
y put) = A₁ ((+) [e²] + [¹] (e")) + A₂ e ²
·A, te + A, et + Aet
y pler= A. ((o)[6²] + [1]6¹) + A₁ e ² + A, et
p(t)
е
S=0
+
t
+
= A₁ te ² + A₁ e ² + A₁ e ² + A. et
е
t
t
= A₁ te ² + 2A₁ e ² +
2A, tet-3A₁e+ + 2 A₂ e ² = te t
~² (2A₁ + -3A₁ + 2A₂) = te ²
e
2A, t-3A, + 2A = t
A₁ (2+-3) + 2A₁ = t
A₁ (2+-3) = t
-A₂ et
A₁te ² + 24 e ² + A₂ e² - 5 A, te ² - 5A,e² - SA₂e² + LeA, te ² + LeAge +
= tex
A₁ = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ada53f7-d108-4ff9-920e-f8297ca83713%2F5ec105bd-282c-4c19-bfd7-29ae2acfe989%2Fz3xwtp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4d) y "- 5y' + by = te ²
(1-2)(x-3) = 0
r₁ = 2
r₂ = 3
m=1
Yo (t) = ( A₁ t`'+ A₂) e +
= A₁ te ¹ + A₂e *
y put) = A₁ ((+) [e²] + [¹] (e")) + A₂ e ²
·A, te + A, et + Aet
y pler= A. ((o)[6²] + [1]6¹) + A₁ e ² + A, et
p(t)
е
S=0
+
t
+
= A₁ te ² + A₁ e ² + A₁ e ² + A. et
е
t
t
= A₁ te ² + 2A₁ e ² +
2A, tet-3A₁e+ + 2 A₂ e ² = te t
~² (2A₁ + -3A₁ + 2A₂) = te ²
e
2A, t-3A, + 2A = t
A₁ (2+-3) + 2A₁ = t
A₁ (2+-3) = t
-A₂ et
A₁te ² + 24 e ² + A₂ e² - 5 A, te ² - 5A,e² - SA₂e² + LeA, te ² + LeAge +
= tex
A₁ = 0
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