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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. x' = 4x + 5y-z y' = x+Z z' = 6x-22y + 10z

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 4x + 5y-z y' = x+Z z' = 6x-22y + 10z

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. x' = 4x + 5y-z y' = x+Z z' = 6x-22y + 10z Eliminate y and z from the system (by first eliminating z and then eliminating y), and solve the remaining differential equation for x. Choose the correct answer below. OA. X(t)=C₁e-3t+C₂e5t + C₂e-t 6t OB. X(t)=C₁e³t+C₂te³t+C₂е¯ OC. X(t)=C₁e³t+C₂e³t+C₂te³t OD. X(t)=C₁e³t+C₂e³t+C₂e³t O E. The system is degenerate. 6t Now find y(t) and z(t) so that y(t), z(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 boxes to complete your choice. O A. y(t)=z(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. x' = 4x + 5y-z y' = x+Z z' = 6x-22y + 10z Eliminate y and z from the system (by first eliminating z and then eliminating y), and solve the remaining differential equation for x. Choose the correct answer below. OA. X(t)=C₁e-3t+C₂e5t + C₂e-t 6t OB. X(t)=C₁e³t+C₂te³t+C₂е¯ OC. X(t)=C₁e³t+C₂e³t+C₂te³t OD. X(t)=C₁e³t+C₂e³t+C₂e³t O E. The system is degenerate. 6t Now find y(t) and z(t) so that y(t), z(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 boxes to complete your choice. O A. y(t)=z(t)= | OB. The system is degenerate.
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