Distinct Real Eigenvalues
In Problems 1–12 find the general solution of the given system.
11.
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- 8. Find the matrix exponential eat, where -1 −1 1 -3 (a) A = =[ (b) A = (c) A = =[ (d) A = -1 2 2 -1 03 00 23 02 Use et to find explicitly the solution of the initial value problem X(0) = [] X' = AX, X (0)arrow_forwardQuestion 2.7a. Consider the linear system of differential equations x' = 4x − 6y y' = 2x 2x - 4y Select the eigenvalues associated with this system. -1 2 3 1 -2arrow_forward8.2 I only need number 22 pleasearrow_forward
- Example 1. Show that the solutions of the following system of differential equations remain bounded as t 00: -uarrow_forwardin picarrow_forwardProblem 11. (9.2/22-26) For each of the linear systems in A through E, find the matching phase portrait (to the right). Briefly justify your choices by examining the eigenvalues. A. X(+1)=[-2.5 0.5]x(1) B. X(+1)=[-2.5 0.5]x(1) C. 3 c. dx-[-2.5 0.5]* dx D. [15]* E. dx # - [3 ]x dt 2 1 III o A 2 1- VII O IF 1-2 4 - 110 -1 IV of VI OF -t VIII O -IE I 3arrow_forward
- Use (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 X' = 0. X(t) =arrow_forwardq14. true or false ?arrow_forwardYou are given the following system of differential equations: dx/dy = 6x + 2y, dy/dt = 2x + 9y You are told that the coefficient matrix is: [6 2] [2 9] and this matrix has eigenvectors: [1] and [-2][2] [1] and the corresponding eigenvalues of 10 and 5. What is the general solution of this system?arrow_forward
- 8. Use Eigenvalue method to find the solution of the following IVP. %3D 4x Y ; r(0) = 1, y(0) = -2 %3D 6x %3D |arrow_forward3. Find the general solution of the system of differential equations x- (10 6 d 8 -5 X= dt cos(7t) – 7 sin(7t) 10 cos(7t) 7 cos(7t) + sin(7t) ) 10 sin(7t) + 4t³e7t + 8t e7t Hint: The characteristic polynomial of the coefficient matrix is X2 – 14A + 98. Moreover cos(7t) – 7 sin(7t) 10 cos(7t) ( 7 cos(7t) + sin(7t) 10 sin(7t) Xp(t) = tªe7t + t°e7t is a particular solution of the system.arrow_forwardSolve 6 and 9 pleasearrow_forward
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