Page #2 se the method of eigenvalues and eigenvectors to find the general solution of the...
Differential equations- please show how to get eigenvectors after getting the eigenvalues and general solution 2 Find the general solution of the following linear systems. (1) X' = -a? where a is a non-zero constant. (2) X, 1 1 X®=(19)*
The matrix has eigenvalues 11 = -7 and 12 = 2. Find eigenvectors corresponding to these eigenvalues. and v2 = help (matrices) Find the solution to the linear system of differential equations * = -25x - 18y y = 27x + 20y satisfying the initial conditions (0) = 4 and y0) = -5. help (formulas) help (formulas)
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or -1 2 2 -1 (i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or -1 2 2 -1
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. (iii) State whether the origin is a node, saddle, center, or spiral. For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. |(iii) State whether the origin is a node, saddle, center, or spiral. Problem 1:...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and 2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or otherwise find the general solution of the system = 4x + 2y = 3x - y 195 marks 5. (a) Give a precise definition of Laplace transform of a function f(t). Use your definition to determine the Laplace transform of 3. Osts 2 6-t, 2 <t f(t) = [20 marks] (b) A logistic initial value problem is given by dP dt kP(M-P), P(0) -...
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b) Solve the initial value problem: dx/dt = 4x + 2y dy/dt = 3x - y with x(0) = 0, y(0) = 7
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, + 2x2 + 2xz x2 = x + 4x2 + x3 X;' =-2x, - 4x2 – x3