Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y" +10y' +34y= 11t³ e - 5t sin 3t What is/are the root(s) of the auxiliary equation associated with the given differential equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. There are no roots to the associated auxiliary equation. OB. The associated auxiliary equation has the double root OC. The associated auxiliary equation has the two roots (Use a comma to separate answers as needed.) Write the form of a particular solution. Choose the correct answer below. C OA. Yp(t)=t(Agt² + A₂t² + A₁t+ A₂) e −5t cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) e -5t sin 3t OB. Yp(t)=t(A₂t³ + A₂t² + A₁t+ A₂) est cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) est sin 3t ○ C. Yp(t) = (A₂t³ + A₂t² +A₁t+ A₂) e ³¹ cos 3t+ (B³t³ + B₂t² + B₁t+B₁) e 5t sin 3t OD. Yp (t) = (A₂t³ +A₂t² +A₁t+Ao) e -5l cos 3t+ (B3t³ + B₂t² + B₁t+Bo) e -5t sin 3t
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y" +10y' +34y= 11t³ e - 5t sin 3t What is/are the root(s) of the auxiliary equation associated with the given differential equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. There are no roots to the associated auxiliary equation. OB. The associated auxiliary equation has the double root OC. The associated auxiliary equation has the two roots (Use a comma to separate answers as needed.) Write the form of a particular solution. Choose the correct answer below. C OA. Yp(t)=t(Agt² + A₂t² + A₁t+ A₂) e −5t cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) e -5t sin 3t OB. Yp(t)=t(A₂t³ + A₂t² + A₁t+ A₂) est cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) est sin 3t ○ C. Yp(t) = (A₂t³ + A₂t² +A₁t+ A₂) e ³¹ cos 3t+ (B³t³ + B₂t² + B₁t+B₁) e 5t sin 3t OD. Yp (t) = (A₂t³ +A₂t² +A₁t+Ao) e -5l cos 3t+ (B3t³ + B₂t² + B₁t+Bo) e -5t sin 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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Transcribed Image Text:Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.)
y" +10y' +34y= 11t³ e
- 5t
sin 3t
What is/are the root(s) of the auxiliary equation associated with the given differential equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. There are no roots to the associated auxiliary equation.
OB. The associated auxiliary equation has the double root
OC. The associated auxiliary equation has the two roots
(Use a comma to separate answers as needed.)
Write the form of a particular solution. Choose the correct answer below.
C
OA. Yp(t)=t(Agt³ + A₂t² + A₁t+ A₂) e −5t cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) e -5t sin 3t
OB. Yp(t)=t(A₂t³ + A₂t² + A₁t+ A₂) est cos 3t+t(B₂t³ + B₂t² + B₁t+Bo) est sin 3t
○ C. Yp(t) = (A₂t³ + A₂t² +A₁t+ A₂) e ³¹ cos 3t+ (B³t³ + B₂t² + B₁t+B₁) e 5t sin 3t
OD. Yp (t) = (A₂t³ +A₂t² +A₁t+Ao) e -5l cos 3t+ (B3t³ + B₂t² + B₁t+Bo) e -5t sin 3t
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