Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = x-y y' = y - 4x C Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. OA. y(t) = C₁ e ¹+₂e-3t OB. y(t) = C₁ e t+C₂ e ³t OC. y(t)=C₁ et+C₂te t OD. y(t) = C₁ e ³t+C₂te³t OE. 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. ⒸA. x(t)= OB. 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' = x-y y' = y - 4x C Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. OA. y(t) = C₁ e ¹+₂e-3t OB. y(t) = C₁ e t+C₂ e ³t OC. y(t)=C₁ et+C₂te t OD. y(t) = C₁ e ³t+C₂te³t OE. 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. ⒸA. x(t)= OB. 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' = x-y
y' = y - 4x
C
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.
-3t
O A. y(t)=C₁ e ¹ + C₂ e
O B. y(t) = C₁ e
OC. y(t) = C₁ e ¹+C₂te
-t+ 3t
+ C₂ e
-t
3t
OD. y(t) = C₁ e ³t+C₂te
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.
ⒸA. x(t)=
OB. The system is degenerate.
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