Jse the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. dx = e dt d²y 6x + = 0 dt OA. X(t) = C, e - 2t + C, e 3 . e5t 24 B. x(t) = C, e 2t + C2 e -3t 5t 24 O C. x(t) = C, e2t cos (3t) + C, e 2t sin (3 24 (3t) + e 5t 5 O D. x(t) = C, e 3t cos (2t) + C, e 3t sin (2t) + St 24 e O E. The system is degenerate. Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. y(t) =D O B. The system is degenerate.
Jse the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. dx = e dt d²y 6x + = 0 dt OA. X(t) = C, e - 2t + C, e 3 . e5t 24 B. x(t) = C, e 2t + C2 e -3t 5t 24 O C. x(t) = C, e2t cos (3t) + C, e 2t sin (3 24 (3t) + e 5t 5 O D. x(t) = C, e 3t cos (2t) + C, e 3t sin (2t) + St 24 e O E. The system is degenerate. Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. y(t) =D O B. The system is degenerate.
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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![**Problem 5.2.16**
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \).
\[
\frac{dx}{dt} + x + \frac{dy}{dt} = e^{5t}
\]
\[
6x + \frac{d^2y}{dt^2} = 0
\]
**Options for \( x(t) \):**
- **A.** \( x(t) = C_1 e^{-2t} + C_2 e^{3t} + \frac{5}{24} e^{5t} \)
- **B.** \( x(t) = C_1 e^{2t} + C_2 e^{-3t} + \frac{5}{24} e^{5t} \) ✔
- **C.** \( x(t) = C_1 e^{2t} \cos(3t) + C_2 e^{2t} \sin(3t) + \frac{5}{24} e^{5t} \)
- **D.** \( x(t) = C_1 e^{3t} \cos(2t) + C_2 e^{3t} \sin(2t) + \frac{5}{24} e^{5t} \)
- **E.** The system is degenerate.
Now find \( y(t) \) so that \( y(t) \) and the solution for \( x(t) \) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( y(t) = \) [Text Box]
- **B.** The system is degenerate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73d5c005-90a3-445f-a212-af9c00b9cb08%2Fcdd88c2f-be75-434b-83db-01ea79e76328%2Fqsthpz6_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 5.2.16**
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \).
\[
\frac{dx}{dt} + x + \frac{dy}{dt} = e^{5t}
\]
\[
6x + \frac{d^2y}{dt^2} = 0
\]
**Options for \( x(t) \):**
- **A.** \( x(t) = C_1 e^{-2t} + C_2 e^{3t} + \frac{5}{24} e^{5t} \)
- **B.** \( x(t) = C_1 e^{2t} + C_2 e^{-3t} + \frac{5}{24} e^{5t} \) ✔
- **C.** \( x(t) = C_1 e^{2t} \cos(3t) + C_2 e^{2t} \sin(3t) + \frac{5}{24} e^{5t} \)
- **D.** \( x(t) = C_1 e^{3t} \cos(2t) + C_2 e^{3t} \sin(2t) + \frac{5}{24} e^{5t} \)
- **E.** The system is degenerate.
Now find \( y(t) \) so that \( y(t) \) and the solution for \( x(t) \) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( y(t) = \) [Text Box]
- **B.** The system is degenerate.
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