In Exercises 11-14, determine the solution to the initial value problem Y' = AY+G(x), Y (0)...

 

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In Exercises 11-14, determine the solution to the initial value problem Y' = AY+G(x), Y (0) = Yo for the given column vector Y (0) and the system Y' = A(x)Y+G(x) in the indicated exercise of this section. 2 -[²] 12. Exercise 2: Yo = [] 11. Exercise 1; Yo = 0 -18 13. Exercise 5; Yo = [3] 1 14. Exercise 6; Yo = In Exercises 11-14, determine the solution to the initial value problem Y' = AY+G(x), Y (0) = Yo for the given column vector Y (0) and the system Y' = A(x)Y+G(x) in the indicated exercise of this section. 2 -[²] 12. Exercise 2: Yo = [] 11. Exercise 1; Yo = 0 -18 13. Exercise 5; Yo = [3] 1 14. Exercise 6; Yo =

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Solutions Step 1 11 We have the system Y AY Gx where A 1 2 3 4 Gx 0 x To solve this system we first need to find the eigenvalues and eigenvectors of A The characteristic polynomial of A is given by de... View the full answer