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 Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. A. y(t) = C₁ e 2 cos 5t + C₂ e 2t 2t OB. y(t) = C₁ e² + C₂te ² + 3 7 -2t sin 5t + cost+ 8 sint 3 7 cost+ sin t 3 7 sin t 8 -21 3 + 7 cost+ sin t ខ C. y(t)=C₁ e 2 cos 5t + C₂ e OD. y(t) = C₁ e 2 + C₂te OE. The system is degenerate. 2t sin 5t+1 cost+g 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. ○ A. x(t)= ○ B. The system is degenerate.
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 Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. A. y(t) = C₁ e 2 cos 5t + C₂ e 2t 2t OB. y(t) = C₁ e² + C₂te ² + 3 7 -2t sin 5t + cost+ 8 sint 3 7 cost+ sin t 3 7 sin t 8 -21 3 + 7 cost+ sin t ខ C. y(t)=C₁ e 2 cos 5t + C₂ e OD. y(t) = C₁ e 2 + C₂te OE. The system is degenerate. 2t sin 5t+1 cost+g 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. ○ A. x(t)= ○ 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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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+ sint
y' = 25x-3y-cost
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.
A. y(t) = C₁ e 2 cos 5t + C₂ e
2t
2t
OB. y(t) = C₁ e² + C₂te ² +
3
7
-2t
sin 5t +
cost+ 8 sint
3
7
cost+
sin t
3
7
sin t
8
-21
3
+
7
cost+ sin t
ខ
C. y(t)=C₁ e 2 cos 5t + C₂ e
OD. y(t) = C₁ e 2 + C₂te
OE. The system is degenerate.
2t sin 5t+1 cost+g
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.
○ A. x(t)=
○ B. The system is degenerate.
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