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Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + y' = 3x + 3y + e-t x' + y'= - 6x-3y + et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. A. x(t)=C₁e³t+C₂e 3t - 3t + 1 5 e -t 5 1 3t B. x(t) = C₁e³t cos (3t) + C₂e³t sin (3t) + 5 C. X(t)= C₁ cos (3t) + C₂ sin (31) 1 D. x(t)=C₁ cos (3t) + C₂ sin (3t) + -t e + -t 1 1 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. 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' = 3x + 3y + e-t x' + y'= - 6x-3y + et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. A. x(t)=C₁e³t+C₂e 3t - 3t + 1 5 e -t 5 1 3t B. x(t) = C₁e³t cos (3t) + C₂e³t sin (3t) + 5 C. X(t)= C₁ cos (3t) + C₂ sin (31) 1 D. x(t)=C₁ cos (3t) + C₂ sin (3t) + -t e + -t 1 1 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. y(t) =

Advanced Engineering Mathematics
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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Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + y' = 3x + 3y + e-t x' + y'= -6x - 3y + et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. 3t A. x(t) = C₁e³t+C₂e -3t + 1 5 -t e 1 5 1 3t B. x(t) = C₁e³t cos (3t) + С₂e³t sin (3t) + C. X(t) = C₁ cos (3t) + C₂ sin (31) -t D. x(t)= C₁ cos (3t) + C₂ sin (3t) + 3t) + = = e² е 1 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. y(t) =
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' = 3x + 3y + e-t x' + y'= -6x - 3y + et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. 3t A. x(t) = C₁e³t+C₂e -3t + 1 5 -t e 1 5 1 3t B. x(t) = C₁e³t cos (3t) + С₂e³t sin (3t) + C. X(t) = C₁ cos (3t) + C₂ sin (31) -t D. x(t)= C₁ cos (3t) + C₂ sin (3t) + 3t) + = = e² е 1 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. y(t) =
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