Use the Method of Undetermined coefficients to solve the system X'=AX+F where...

Question

4 2 -15

A= ( ) , F(t)= ( ) *te^(-2t)

3 -1 -4

Answer 1

1st Order Linear ODE Statement

Definitions

Method of Undetermined Coefficients

Homogeneous Solution

General Formulas for Solving

Homogeneous Solution Formula

Matrix Exponential

Diagonalizing Matrix

Particular Solution Formula

Particular Solution must not match Homogenous

Solve: Find eigenvalues of A

Theory of eigenvectors

Solve: Find eigenvectors of A

Solve: Find diagonalizing matrix P

Solve: Find inverse of matrix P

Solve: Calculate matrix exponential

Solve: Find homogenous solution.

Start of particular solution

Solve: Particular solution, first guess

Solve: Particular solution, second guess

Solve: Second guess derivative

Solve: Insert derivative and second guess to main equation

Solve: Split into 3 equations

Solve: t^2 equation

Solve: t equation and constants equation

Combine homogeneous and particular solutions