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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'=7x+6y +et x'+y'= -5x-3y + e¹ Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. OA. x(t) = C₁ cos (3t) + C₂ sin (3t) B. x(t) = C₁ cos (3t) + C₂ sin (3t) + = €¯²¹ + = ²² OC. X(t)=C₁e³t+C₂e-³ + 5 ○ D. x(t) = C₁³¹ cos (3t) + C₂e³¹ sin (3t) + ½e¹-e¹ 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) = - 31 -t

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + y'=7x+6y +et x'+y'= -5x-3y + e¹ Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. OA. x(t) = C₁ cos (3t) + C₂ sin (3t) B. x(t) = C₁ cos (3t) + C₂ sin (3t) + = €¯²¹ + = ²² OC. X(t)=C₁e³t+C₂e-³ + 5 ○ D. x(t) = C₁³¹ cos (3t) + C₂e³¹ sin (3t) + ½e¹-e¹ 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) = - 31 -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' = 7x+6y + et x' + y'= -5x - 3y + e¹ Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. x(t) = C₁ cos (3t) + C₂ sin (31) O A. B. x(t) = C₁ cos (3t) + C₂ sin (3t) +5e + - 3t OC. X(t) = C₁e³t+C₂е¯ + 1 5⁰ -t 1 3t © D. x(t) = C₁e³t cos (3t) + C₂e³t sin (3t) + ½e-¯ 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' = 7x+6y + et x' + y'= -5x - 3y + e¹ Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. x(t) = C₁ cos (3t) + C₂ sin (31) O A. B. x(t) = C₁ cos (3t) + C₂ sin (3t) +5e + - 3t OC. X(t) = C₁e³t+C₂е¯ + 1 5⁰ -t 1 3t © D. x(t) = C₁e³t cos (3t) + C₂e³t sin (3t) + ½e-¯ 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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