Solve the system of differential equations 1' - 1x₁ - 6x2 X2' = 1x₁ + 4x2 x₁(0) = − 6, x₂(0) - = 2 x₁ (t) = x₂(t) =
Solve the system of differential equations 1' - 1x₁ - 6x2 X2' = 1x₁ + 4x2 x₁(0) = − 6, x₂(0) - = 2 x₁ (t) = x₂(t) =
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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![### Solve the System of Differential Equations
Given:
\[
\begin{cases}
x_1' = -1x_1 - 6x_2 \\
x_2' = 1x_1 + 4x_2
\end{cases}
\]
With initial conditions:
\[
x_1(0) = -6, \quad x_2(0) = 2
\]
Complete the solution by finding \( x_1(t) \) and \( x_2(t) \):
\[ x_1(t) = \ \_\_\_\_\_ \]
\[ x_2(t) = \ \_\_\_\_\_ \]
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Transcribed Image Text:### Solve the System of Differential Equations
Given:
\[
\begin{cases}
x_1' = -1x_1 - 6x_2 \\
x_2' = 1x_1 + 4x_2
\end{cases}
\]
With initial conditions:
\[
x_1(0) = -6, \quad x_2(0) = 2
\]
Complete the solution by finding \( x_1(t) \) and \( x_2(t) \):
\[ x_1(t) = \ \_\_\_\_\_ \]
\[ x_2(t) = \ \_\_\_\_\_ \]
##### Additional Support
If you need help with this problem, feel free to contact the instructor by clicking on "Message instructor."
### [Submit Question]
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