Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x+y'-8x-8y = e−2t x'+y'+4x+2y= e8t Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. A. x(t)=C₁et+C2e-4t 4t OB. x(t) = C₁et cos 4t + C₂et sin 4t c. x(t) = C₁ cos 4t + C₂ sin 4t D. x(t) = C₁et + C₂te 4t OE. The system is degenerate. 2 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find y(t)
Use the elimination method to find a general solution for the given linear system, where differentiation is with
respect to t.
2x+y'-8x-8y = e-2t
x'+y' + 4x+2y= e8t
Eliminate y and solve the remaining differential equation for x. Choose the correct answer below.
A. x(t)=C₁et + Cze
- 4t
B. x(t) = C₁et cos 4t + C₂et sin 4t
c. x(t) = C₁ cos 4t+ C2 sin 4t
OD. x(t)=C₁et + C₂te 4t
ง
OE. 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.
OA. y(t) =
OB. The system is degenerate.
Transcribed Image Text:Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x+y'-8x-8y = e-2t x'+y' + 4x+2y= e8t Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. A. x(t)=C₁et + Cze - 4t B. x(t) = C₁et cos 4t + C₂et sin 4t c. x(t) = C₁ cos 4t+ C2 sin 4t OD. x(t)=C₁et + C₂te 4t ง OE. 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. OA. y(t) = OB. The system is degenerate.
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