Find the solution for the system that satisfies the conditions at t = 0. Y1 + 5y2, y'2 = -5y1 + y'ı = Y1(0) = 3 Y2, Y2(0) = -1 (Y1(t), y2(t))
Find the solution for the system that satisfies the conditions at t = 0. Y1 + 5y2, y'2 = -5y1 + y'ı = Y1(0) = 3 Y2, Y2(0) = -1 (Y1(t), y2(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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![**Problem Statement:**
Find the solution for the system that satisfies the conditions at \( t = 0 \).
**Differential Equations:**
\[
y_1' = y_1 + 5y_2, \quad y_1(0) = 3
\]
\[
y_2' = -5y_1 + y_2, \quad y_2(0) = -1
\]
**Solution:**
\[
(y_1(t), y_2(t)) = \left( \boxed{\phantom{\text{solution space}}} \right)
\]
**Explanation:**
The above represents a first-order linear differential equation system. The task is to determine the functions \( y_1(t) \) and \( y_2(t) \) given the initial conditions \( y_1(0) = 3 \) and \( y_2(0) = -1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad35cd49-88f1-4759-9e4c-232c0c792d3e%2F2f37e96f-22ca-40a7-956f-97ce29893485%2F4rvt1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the solution for the system that satisfies the conditions at \( t = 0 \).
**Differential Equations:**
\[
y_1' = y_1 + 5y_2, \quad y_1(0) = 3
\]
\[
y_2' = -5y_1 + y_2, \quad y_2(0) = -1
\]
**Solution:**
\[
(y_1(t), y_2(t)) = \left( \boxed{\phantom{\text{solution space}}} \right)
\]
**Explanation:**
The above represents a first-order linear differential equation system. The task is to determine the functions \( y_1(t) \) and \( y_2(t) \) given the initial conditions \( y_1(0) = 3 \) and \( y_2(0) = -1 \).
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