4. Write the initial value problem in matrix form X' = AX + f(t), X (to)...
Problem 1. x(1) 67 (1 point) Given X = AX with X(t) = , A = and x(0) = Vt)] -20 91 (a) Write the eigenvalues and eigenvectors of A (b) Write the solution of the initial-value problem in terms of xt), y(t) x(t) = yt) =
Write the given system in the matrix form x' = Ax+f. r(t) = 7r(t) + tant e' (t) = r(t) - 90(t) – 5 Express the given system in matrix form.
dy 3. (10 points) Solve the initial value problem - dr answer in the form y=f(x). Show your work. + 2y = In z with y(1) = -6. Give your final
5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' Ax. Find the directions of greatest attraction and/or repulsion 12 16 A= 8 12 Solve the initial value problem. x(t) 5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an...
, i-N points ZiDiffEQModAp10 8.3 031 Recall from (14) in Section 8.3 that associated homogeneous system. Use the above to solve the given initial-value pro t) is a fundamental matrix of the AX + F(t), X(to)-Xo whenever φ( solves the initial value problem X'- 5 31x+ X(t)- Submit Answer Save Progress , i-N points ZiDiffEQModAp10 8.3 031 Recall from (14) in Section 8.3 that associated homogeneous system. Use the above to solve the given initial-value pro t) is a fundamental...
Consider the matrix A. A = Write the general solution of the system x'(t) = Ax(t) in the form x(t) = C,x,(t) + Cox,(t). Enter any column vector xce) = cze-34–1,1) + cze +36(84–1,1)+(-1,0))
Solve the given initial-value problem. The DE is of the form dy dx = f(Ax + By + C). dy dx = 5x + 4y 5x + 4y + 4 , y(−1) = −1
Write in matrix notation the canonical form of the following linear programming problem: Maximise z=x+y subject to x+2y 59 2x+y<9 x20,y20
Answer All questions please QUESTION FOUR Consider the initial value problem x(t) A(t)x(t) f(t), dt where xo is some constant vector (a) Show that the associated homogenous system, x(t) A(t)x(t), has its transi tion matrix as X(t)e Ar)dr provided AeJtr)-Ar) A(t) for all t 10 Marks A(t) A(T)dr (b) Obtain a solution to the initial value problem, given that ()- () 4 A = 6 et and x(0) 1 15 Marks f(t) QUESTION FOUR Consider the initial value problem x(t)...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...