Please answer a. - e. You are given a homogeneous system of first-order linear differential equations...
Exercise 1 Consider the system of differential equations 2 x= ( _ _3.)* (1) and let x("(t) = ( - ) 2 and x2(t) = ( _)er. a) Show that x(1) and x(2) are solutions of (1). b) Show that x = cıx(1) + c2x(2) is also a solution of (1) for any constants ci and c2. c) Show that x(1) and x(2) form a fundamental set of solutions. d) Find the solution of (1) that satisfies the initial condition...
Find the real valued solution to the linear system of differential equations a Find the most general real-valued solution to the linear system of differential equations 1(t) 22(t) =c1 C2
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
Given the non-homogeneous linear system of differential equations ? ′ = −2? − 7? + 3? ?′=−? +4? +?-6t Find its homogeneous solution using the eigenvalue-eigenvector approach (10pts) Use the variation-of-parameters method to find its particular solution (10pts)
8. Solve the following first order homogeneous linear system of differential equations I a -B -B Cu = -3 4 -3 | u, 1-B –B a ) where a and B are real nonzero constants. Find a fundamental matrix and the inverse matrix of the fundamental matrix. Hint: dot1 TI 212/1 a 22).
Find the general solution to the linear system of non-homogeneous differential equations x = x + x + 1 xz' = 3x1 - x2 +t
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1 11 1 1 u-et 1 1 2 3 First of all, find a fundamental matrix and the inverse matrix of the fundamental matrix of the corresponding homogeneous linear system. Then given a particular solution 71 uy(t) = et 1 2 find the general solution of the nonhomogeneous linear system of differential equations. Hint: det(A - \I) = -(1 – 2)?(1+1)
Given the non-homogeneous linear system of differential equations Xi' = -2x1 – 7x2 + 3t xz' = -X1 + 4x2 + e-6 a. Find its homogeneous solution using the eigenvalue-eigenvector approach b. Use the variation-of-parameters method to find its particular solution
Given the non-homogeneous linear system of differential equations Xi' = -2x1 – 7x2 + 3t xz' = -X1 + 4x2 + e-6 a. Find its homogeneous solution using the eigenvalue-eigenvector approach b. Use the variation-of-parameters method to find its particular solution
8. Given the non-homogeneous linear system of differential equations x1' = -2x1 - 7x2 + 3t X2 = -X1 + 4x2 + e-6 a. Find its homogeneous solution using the eigenvalue-eigenvector approach (10pts) b. Use the variation-of-parameters method to find its particular solution (10pts)