Consider the initial value problem y, j(0) = a. Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v1 = , 02 = Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. y(t) = c1 + c2

Consider the initial value problem y, j(0) = a. Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v1 = , 02 = Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. y(t) = c1 + c2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Suppose A is a 2 × 2 real matrix with an eigenvalue A = 1+ 4i and corresponding eigenvector -1+i Determine a fundamental set (i.e., linearly independent set) of solutions for y' = Aj, where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. 1 ÿ1(t) ý2(t) =
2. Given the system dx₁ dt dx dt C. = 3x₂ + 3x₂ -= 4x₁ - 1x₂ a. Write the above system in matrix form ie = Ax. What is A? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = (3) e. Give the solution of the IVP with initial value x(1) = 3 using e¹A
Consider the second-order equation d 2y/dt 2 + p dy/dt +qy = 0 a. If p=q=1, compute the eigenvalues and eigenvectors of the coefficient matrix. What would be the long-term behavior of the solutions in this case? b. If p=0 and q=2 determine the general solution.
a. Find the eigenvalues and eigenvectors of the matrix x₁ (t) x₂ (t) = X₁ b. Solve the system of differential equations a' = = = V₁ = [₁ 5 -3 4 -2 and X₂ = satisfying the initial conditions V₂ = [₁8] =[3]
Suppose that the matrix A has the following eigenvalues and eigenvectors:
do not copy
2x + 3y + 6z = 3 + 2y + 2z = −1 using 3x - 4y - 5z = -6 B. Solve the linear system-x 1. Cramer's rule 2. inverse matrix 3. LU decomposition
Linear algebra: please correctly and handwritten
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 6x + 7y=0 y" - 2x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. X₁ = x¹, x₂ = y' O B. X₁ =X, X2₂=X'', X3 = Y, X4 =y" O c. x₁ = x¹, x₂ = x¹, X3 = y', X4 =y" O D. x₁ = x, X₂ = x', X3 = Y, X4 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. B. X₁ X₂ X₁ S w X4 || X₁ X2 x1 3 ... W X4 ро
Consider the linear system dx₁ dt dx₂ dt = 4x1 - 3x₂ = 3x1 + 4x2. 1. Show that upon conversion to the form X'= AX, the eigenvalues of A are complex. 2. Find the general solution of the system.
Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 5i and corresponding eigenvector i * = (-²+1). v= Determine a fundamental set (i.e., linearly independent set) of solutions for ÿ' = Aỹ, where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. (t) = 2(t) = → - →
) Consider the linear system X₁ = Y a. Find the eigenvalues and eigenvectors for the coefficient matrix. 18 v1 = b. Find the real-valued solution to the initial value problem {{{ = -3 -2 5 -3] Use t as the independent variable in your answers. y₁ (t) Y₂ (t) - 3y1 - 2y2, 5y1 + 3y2, y." , and X₂ = V2 y₁ (0) = 9, Y₂ (0) = -10. ||