24. Let A be a 2 x 2 real constant coefficient matrix. Suppose the system of...
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)...
Determine e At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(0)1. 0 2 2 2 0 2 2 2 0 First, find X(t). Choose the correct answer below 4t -2t 4t e -2t (1+t) e e -2t OA. X(t) (1+t)e4t 0 e2t B. X(t)= e4t 0 -2t -2t 2t - e - 2t (1t)e 4t e e 4t e 4t - sint sin t 0 (1t)e -2t O C....
The 2 x 2 matrix A -3 2 -1 -1) has complex eigenvalues r = -2+i. An eigenvector corresponding to r = -2+i is The system x' = Ax+ -24 e- has one solution given by x(t) = (2) e-2t. What is the general solution to the system? OA -20 cost sint - cost st) + C2 sint sint - cost e-2t + (1). e-27 och cost e-24 + C3 (2 ) e-24 cost * (sin e tez (-sind) e...
DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. Here is an example of what the answer should look like. The answer should be in this form. example 7x 9.7.15 Question Help Use the variation of parameters formula to find a general...
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. 4 - 1 4 + 4t Let x(t) = xn (t) + xp (t), where xn (t) is the general solution corresponding to the homogeneous system, and xo(t) is a particular solution to the nonhomogeneous system. Find Xh(t) and xp(t). Xh(t) = U. Xp(t) = 0
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. 9.7.15 Question Help 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. - 16 1 A=...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2 with vi = and |_ G 12 = -2 with v2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) (50) = C1 + C2 e e B. In fundamental matrix form: (MCO) = I: C. As two equations: (write "c1" and "c2" for C1 and c2) x(t) = yt) =
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...