Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficie y" -6y' +9y=19t6 e ³t ... What are the roots of the auxiliary equation associated with the given differential equation? OA. The associated auxiliary equation has the two roots (Use a comma to separate answers as needed.) OB. The associated auxiliary equation has the double root O c. There are no roots to the associated auxiliary equation. Write the form of a particular solution. Choose the correct answer below. 3t 31² O A. y(t) = = (A6t6 + A515 + A4tª + A3t³ + A₂₁² + A₁t+Ao) e ³ OB. y(t) = (A6t6 +A5t5 + A₁t¹ + A₂t³ + A₂₁² + A₁t+ A₂) e Oc. y(t)=12 (A6t6+A515 + A₁t4 + A3t³ + A₂1² + A₁t+Ap t+Ao) e e 3t D. y(t)=t(A6t6 + A₁t5 +A414 + A3t³ + A₂t² + A₁t+ A₁) e² 3t
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficie y" -6y' +9y=19t6 e ³t ... What are the roots of the auxiliary equation associated with the given differential equation? OA. The associated auxiliary equation has the two roots (Use a comma to separate answers as needed.) OB. The associated auxiliary equation has the double root O c. There are no roots to the associated auxiliary equation. Write the form of a particular solution. Choose the correct answer below. 3t 31² O A. y(t) = = (A6t6 + A515 + A4tª + A3t³ + A₂₁² + A₁t+Ao) e ³ OB. y(t) = (A6t6 +A5t5 + A₁t¹ + A₂t³ + A₂₁² + A₁t+ A₂) e Oc. y(t)=12 (A6t6+A515 + A₁t4 + A3t³ + A₂1² + A₁t+Ap t+Ao) e e 3t D. y(t)=t(A6t6 + A₁t5 +A414 + A3t³ + A₂t² + A₁t+ A₁) e² 3t
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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1 Differential equations
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Transcribed Image Text:Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficie
y'' -6y' +9y= 19t6 e 3t
What are the roots of the auxiliary equation associated with the given differential equation?
O A.
The associated auxiliary equation has the two roots
(Use a comma to separate answers as needed.)
B. The associated auxiliary equation has the double root
Oc. There are no roots to the associated auxiliary equation.
Write the form of a particular solution. Choose the correct answer below.
A. y(t) = = (A6t6 + Ast5 + A4t¹ + A₂t³ + A₂t² + A₁t+ A₁)
3t
e
OB. y(t) =
+ A₁t+A₁)
31²
e
= (A6t6 + A5₁5 + A₁t¹ + A₂₁³ + A₂1² +/
O c. y(t) = 1² (A6t6 + A51³ + A₁tª + A3t³ + A₂1² + A₁t+A₁)
OD. y(t)=t(A6t6 + A₁t³ + A₁¹¹ + A₂t³ + A₂₁² + A₁t+ Ao) e²
3t
e
e 3t
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