For all the problems below, just find the correct solution form for the particular solution to the differential equation if the method of undetermined coefficients were used. No need to solve for the coefficients in the particular solution. Just write the particular solution form with A0, A₁, A₂, etc. left in it. Problem 1 (Exercise 2.6.74) x" + 3x'- 10x = 1² cost Problem 2 (Exercise 2.6.70) Problem 3 (Exercise 2.6.86) x" - 6x' +5x=e5t + 1²e-5t x"+x=et- et + et cost
For all the problems below, just find the correct solution form for the particular solution to the differential equation if the method of undetermined coefficients were used. No need to solve for the coefficients in the particular solution. Just write the particular solution form with A0, A₁, A₂, etc. left in it. Problem 1 (Exercise 2.6.74) x" + 3x'- 10x = 1² cost Problem 2 (Exercise 2.6.70) Problem 3 (Exercise 2.6.86) x" - 6x' +5x=e5t + 1²e-5t x"+x=et- et + et cost
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![## Differential Equations: Problem Set
For all the problems below, identify the correct solution form for the particular solution to the differential equation using the method of undetermined coefficients. There is no need to solve for the coefficients in the particular solution. Write the particular solution form with \( A_0, A_1, A_2, \) etc., as placeholders.
### Problem 1 (Exercise 2.6.74)
\[
x'' + 3x' - 10x = t^2 \cos t
\]
### Problem 2 (Exercise 2.6.70)
\[
x'' - 6x' + 5x = e^{5t} + t^2 e^{-5t}
\]
### Problem 3 (Exercise 2.6.86)
\[
x'' + x = e^{-t} - e^t + e^t \cos t
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62a79166-ba2c-43d7-9fa1-94c5c5be2063%2Fa98ab88a-0efe-49ae-bb8e-5b11dc6711f6%2Fhb4qjcd_processed.png&w=3840&q=75)
Transcribed Image Text:## Differential Equations: Problem Set
For all the problems below, identify the correct solution form for the particular solution to the differential equation using the method of undetermined coefficients. There is no need to solve for the coefficients in the particular solution. Write the particular solution form with \( A_0, A_1, A_2, \) etc., as placeholders.
### Problem 1 (Exercise 2.6.74)
\[
x'' + 3x' - 10x = t^2 \cos t
\]
### Problem 2 (Exercise 2.6.70)
\[
x'' - 6x' + 5x = e^{5t} + t^2 e^{-5t}
\]
### Problem 3 (Exercise 2.6.86)
\[
x'' + x = e^{-t} - e^t + e^t \cos t
\]
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