(5) (BONUS) For each linear second order system below, write it as first order system and...
**PLEASE USE MATLAB 2. For each system of linear algebraic equations, determine if the system is underdetermined, has an exact solution, or is overdetermined. If the system is underdetermined, find the general solution and then find a particular solution and check your answer. If the system is exact, find the unique solution and check your answer. If the system is overdetermined, find a least squares solution. 3x, + 2x,-4x, + x,-2 -x, +5x2 + 2x, + 3x4 = 4 4x,...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...
2) Just as an nth order equation can be transformed to a system of n first order equations, a system of m n" order equations can be transformed into a system of mn first order equations. Transform the system of two second order equations into a system of first order equations. Again, your variables are x,, X2, X3..... x" + 3x' + 4x – 2y=0, y" + 2y' – 3x + y =é cost, where x = x(t), y =...
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...
5. (15 pts) For the linear system x + 2y + z = 4 2 + 5y + 2z = 3 4x - y +9z = -1 a) Write the system in matrix-vector form Ax = b. b) Form the augmented matrix [ A6] c) Fill-in the necessary row operations to produce each of the following matrices. 4 1 2 1 0 -3 -1 0 9 -5 17 → O CON 1 00-8 4 -1 20 1 2 1 4...
(1 point) In this exercise we consider the second order linear equation y" + series solution in the form y = 0. This equation has an ordinary point at x = 0 and therefore has a power y = cmx". n=0 We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn...
In exercises 9-18 apply elementary equation operations to the given linear system to find an equivalent linear system in echelon form. If the system is consistent then use back substitution to find the general solution. See Method (1.11) and Method (1.1.2) 4x + 3y + z = 0 3x + 2y + z = -2 10. 3x-5y + 2z =-1
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...