Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t dx = x-y dt dy = 4x+y dt Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. ○ A. y(t) = C₁e¯¹ + C₂te¯† ○ B. y(t) = C₁e¹ + C₂tet Oc. y(t)=C₁e cos 2t+ C₂et sin 2t D. y(t)=C₁e cos 2t + C₂e¹ sin 2t 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)= C₁e cos 2t+ + C₂e¹ sin 2t
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t dx = x-y dt dy = 4x+y dt Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. ○ A. y(t) = C₁e¯¹ + C₂te¯† ○ B. y(t) = C₁e¹ + C₂tet Oc. y(t)=C₁e cos 2t+ C₂et sin 2t D. y(t)=C₁e cos 2t + C₂e¹ sin 2t 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)= C₁e cos 2t+ + C₂e¹ sin 2t
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.
dx
= x-y
dt
dy
dt
= 4x+y
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.
○ A. y(t) = C₁e¯¹ + C₂te¯†
○ B. y(t) = C₁e¹ + C₂tet
Oc. y(t)=C₁e cos 2t+ C₂et sin 2t
D. y(t)=C₁e cos 2t+ + C₂e¹ sin 2t
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)=C₁e cos 2t+ + C2e¹ sin 2t
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