Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 7x-2y + sint y' = 25x-3y - cost Write the system in operator form. = sint - cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. 3 - 2t -2t OA. y(t)=C₁e cos 5t+C₂e sin 5t + OB. y(t) = C₁e²t + C₂te²t+cost+ OC. y(t) = C₁ e 2t + C₂te -2t + 3 7 8 cost+ A. X(t)= O B. The system is degenerate. sint 7 8 3 OD. y(t) = C₁e²t cos 5t + C₂e²¹ sin 5t+ 8 cost+ sin t 7 8 C... sin t 7 cost+ sin t 8 O E. The system is degenerate. Now find x(t) so that x(t) and the solution for y(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.
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 7x-2y + sint y' = 25x-3y - cost Write the system in operator form. = sint - cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. 3 - 2t -2t OA. y(t)=C₁e cos 5t+C₂e sin 5t + OB. y(t) = C₁e²t + C₂te²t+cost+ OC. y(t) = C₁ e 2t + C₂te -2t + 3 7 8 cost+ A. X(t)= O B. The system is degenerate. sint 7 8 3 OD. y(t) = C₁e²t cos 5t + C₂e²¹ sin 5t+ 8 cost+ sin t 7 8 C... sin t 7 cost+ sin t 8 O E. The system is degenerate. Now find x(t) so that x(t) and the solution for y(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.
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:Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.
x' = 7x-2y + sin t
y' = 25x-3y - cost
Write the system in operator form.
= sint
= - cost
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.
-2t
O A. y(t) = C₁ e 2t cos 5t + С₂e¯ sin 5t +
8
OB. y(t) = C₁e²t+C₂te²t.
OC. y(t) = C₁ e 2t+C₂te¯
+
3
8
2t
cost +
+
3
8
7
8
O A. X(t) =
OB. The system is degenerate.
sin t
cost+
sin 5t +
7
8
3
7
cost+ sin t
8
OD. y(t) = C₁e²t cos 5t+C₂e²t
O E. The system is degenerate.
Now find x(t) so that x(t) and the solution for y(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.
8
sin t
7
+ sint
cost +
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