Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Finding the General Solution of a Linear System Using the Eigenvalue Method**
To determine the general solution to the differential equation system, you can inspect or factor the eigenvalues of the coefficient matrix. The system of differential equations is as follows:
\[ x_1' = 8x_1 + 3x_2 + 8x_3, \]
\[ x_2' = 3x_1 + 13x_2 + 3x_3, \]
\[ x_3' = 8x_1 + 3x_2 + 8x_3. \]
To find the general solution to this system, denoted in matrix form, we use the eigenvalue method.
The matrix form of the solution is:
\[ \mathbf{x}(t) = \boxed{ }
Explore the steps involved in finding eigenvalues and eigenvectors, and use them to formulate the solution to the system of differential equations.](https://content.bartleby.com/qna-images/question/06bbd155-c9d1-4bdc-8881-0cd893ac016a/f3916c45-e196-4832-b139-7ddf2e98cbba/5g67uo1_processed.png)
Transcribed Image Text:**Finding the General Solution of a Linear System Using the Eigenvalue Method**
To determine the general solution to the differential equation system, you can inspect or factor the eigenvalues of the coefficient matrix. The system of differential equations is as follows:
\[ x_1' = 8x_1 + 3x_2 + 8x_3, \]
\[ x_2' = 3x_1 + 13x_2 + 3x_3, \]
\[ x_3' = 8x_1 + 3x_2 + 8x_3. \]
To find the general solution to this system, denoted in matrix form, we use the eigenvalue method.
The matrix form of the solution is:
\[ \mathbf{x}(t) = \boxed{ }
Explore the steps involved in finding eigenvalues and eigenvectors, and use them to formulate the solution to the system of differential equations.
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