) This is the second part of a three-part problem. Consider the system of differential equations Verify that for any constants C₁ and C2, the functions y₁ (t) Y₂ (t) Y₁ Y₂ = - = = = = 5y₁ + 3y2, 3y₁ + 5y2. satisfy the system of differential equations. Enter c₁ as c1 and c as c2. a. Find the value of each term in the equation y₁ = 5y₁ + 3y2 in terms of the variable t. (Enter the terms in the order given.) C₁e²t + c₂est, -C₁e²t + c₂est, + b. Find the value of each term in the equation y₂ = 3y₁ + 5y2 in terms of the variable t. (Enter the terms in the order given.) +
) This is the second part of a three-part problem. Consider the system of differential equations Verify that for any constants C₁ and C2, the functions y₁ (t) Y₂ (t) Y₁ Y₂ = - = = = = 5y₁ + 3y2, 3y₁ + 5y2. satisfy the system of differential equations. Enter c₁ as c1 and c as c2. a. Find the value of each term in the equation y₁ = 5y₁ + 3y2 in terms of the variable t. (Enter the terms in the order given.) C₁e²t + c₂est, -C₁e²t + c₂est, + b. Find the value of each term in the equation y₂ = 3y₁ + 5y2 in terms of the variable t. (Enter the terms in the order given.) +
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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Transcribed Image Text:) This is the second part of a three-part problem.
Consider the system of differential equations
y₁
Y₂
Verify that for any constants c₁ and c₂, the functions
y₁ (t)
Y₂ (t)
-
=
=
=
5y1 + 3y2,
3y1 + 5y2.
C₁e²t + c₂est,
-C₁e²t+c₂est,
satisfy the system of differential equations. Enter c₁ as c1 and c as c2.
a. Find the value of each term in the equation =
given.)
5y₁ + 3y₂ in terms of the variable t. (Enter the terms in the order
+
b. Find the value of each term in the equation y₂ = 3y₁ + 5y2 in terms of the variable t. (Enter the terms in the order
given.)
+
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