**Problem Statement:**Use the variation of parameters formula to find a general solution of the system $ x'(t) = Ax(t) + f(t) $, where $ A $ and $ f(t) $ are given.**Matrix and Vector Definitions:**\[A = \begin{bmatrix} 1 & 9 \\ 17 & 9 \end{bmatrix}, \quad f(t) = \begin{bmatrix} 5 \\ -5 \end{bmatrix}\]**Objective:**Determine $ x(t) = \begin{bmatrix} \_ \\ \_ \end{bmatrix} $.**Explanation:**The system $ x'(t) = Ax(t) + f(t) $ is a linear non-homogeneous differential equation. The matrix $ A $ is a $ 2 \times 2 $ matrix, and $ f(t) $ is a $ 2 \times 1 $ vector. The solution involves finding a particular solution using the method of variation of parameters along with the complementary (homogeneous) solution. To solve, evaluate and integrate using these elements to achieve the general solution vector $ x(t) $.

We need to find a particular solution to the below system of equation. Here, A=19179, f(t)=5-5. The…

Answered: Use the variation of parameters formula…

Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. 19 A = f(t) = 17 9 x(t) = O

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Problem Statement:**

Use the variation of parameters formula to find a general solution of the system $ x'(t) = Ax(t) + f(t) $, where $ A $ and $ f(t) $ are given.

**Matrix and Vector Definitions:**

\[
A = \begin{bmatrix} 1 & 9 \\ 17 & 9 \end{bmatrix}, \quad f(t) = \begin{bmatrix} 5 \\ -5 \end{bmatrix}
\]

**Objective:**

Determine $ x(t) = \begin{bmatrix} \_ \\ \_ \end{bmatrix} $.

**Explanation:**

The system $ x'(t) = Ax(t) + f(t) $ is a linear non-homogeneous differential equation. The matrix $ A $ is a $ 2 \times 2 $ matrix, and $ f(t) $ is a $ 2 \times 1 $ vector. The solution involves finding a particular solution using the method of variation of parameters along with the complementary (homogeneous) solution. To solve, evaluate and integrate using these elements to achieve the general solution vector $ x(t) $.

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