Transform the given system of differential equations into an equivalent system of first-order differential equations. x" - 3x' -5x + 2y = 0 y'' +6y' - 6x-3y = sin t Let x₁ = x, X₂ = X', Y₁ =y, and y₂ =y'. Complete the system below. X 2 Ź 5 || II
Transform the given system of differential equations into an equivalent system of first-order differential equations. x" - 3x' -5x + 2y = 0 y'' +6y' - 6x-3y = sin t Let x₁ = x, X₂ = X', Y₁ =y, and y₂ =y'. Complete the system below. X 2 Ź 5 || II
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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![Transform the given system of differential equations into an equivalent system of first-order differential equations.
\[ x'' - 3x' - 5x + 2y = 0 \]
\[ y'' + 6y' - 6x - 3y = \sin t \]
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Let \( x_1 = x \), \( x_2 = x' \), \( y_1 = y \), and \( y_2 = y' \). Complete the system below.
\[ x_1' = \, \boxed{} \]
\[ x_2' = \, \boxed{} \]
\[ y_1' = \, \boxed{} \]
\[ y_2' = \, \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F671be518-f9e6-4df9-9304-33791fefeccb%2Ff8e8d6bc-1527-42fc-a206-d89c09a15f6a%2F5nogfjk_processed.png&w=3840&q=75)
Transcribed Image Text:Transform the given system of differential equations into an equivalent system of first-order differential equations.
\[ x'' - 3x' - 5x + 2y = 0 \]
\[ y'' + 6y' - 6x - 3y = \sin t \]
---
Let \( x_1 = x \), \( x_2 = x' \), \( y_1 = y \), and \( y_2 = y' \). Complete the system below.
\[ x_1' = \, \boxed{} \]
\[ x_2' = \, \boxed{} \]
\[ y_1' = \, \boxed{} \]
\[ y_2' = \, \boxed{} \]
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