7. (10 points) Find the general solution to the homogeneous system of DE: x' = Ax...
7. (10 points) Find the general solution to the homogeneous system of DE: -1 x' = Ax where A -2 = [ 21
2 8. (10 points) Find the general solution to the homogeneous system of DE: | 3 x' = Ax where A = -2 1 - 1 -2 -4.
1 -2 Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 1 -2
Use the variation of parameters formula to find a general solution of the system x'(0) AX(t) + f(t), where A and f(t) are given -4 2 А. FU) 21 12 +21 Let x(t) = xy()+ X(t), where x, (t) is the general solution corresponding to the homogeneous system, and X(t) is a particular solution to the nonhomogeneous system. Find X. (t) and X.(1).
Find the general solution to the non-homogeneous system of DE: -4 X+
Find the general solution to the non-homogeneous system of DE: -4 51 3t X + -4 0 x'
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
Find the general solution of the system x' = Ax where A is the given matrix. If an initial condition is given, also find the solution that satisfies the condition. 1.1 5 2 :| -2 1 )
7. Find a Trial Solution for the following System of DE. You must have solved the corresponding homogeneous system in problem number 4.] +2e2t +1 x' = +6x2 x1 7. Find a Trial Solution for the following System of DE. You must have solved the corresponding homogeneous system in problem number 4.] +2e2t +1 x' = +6x2 x1
Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. 2 A= -4 2 ,f(t) = -1 14 +2t - 1 Let x(t) = x (t) + X(t), where xn(t) is the general solution corresponding to the homogeneous system, 1 xp (t) is a particular solution to the nonhomogeneous system. Find xh (t) and xp(t). and 1 -2 Xh(t) = 41 2 1 1 X(t)...