This is the third part of a three-part problem.Consider the system of differential equationswith solutionsỹ (t) =Y{Y₂₁2= C1y₁ (t)Y₂(t)====5y1 + 3y2,3y1 + 5y2,for any constants c₁ and c₂. Rewrite the solution of the equations in vector form asÿ(t) = C₁ÿ₁(t) + C2ÿ2(t).C₁e² + c₂est"-C₁e²t + c₂e8t,+ C2

Answered: This is the third part of a three-part…

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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Question

This is the third part of a three-part problem.
Consider the system of differential equations
with solutions
ỹ (t) =
Y{
Y₂₁2
= C1
y₁ (t)
Y₂(t)
=
=
=
=
5y1 + 3y2,
3y1 + 5y2,
for any constants c₁ and c₂. Rewrite the solution of the equations in vector form as
ÿ(t) = C₁ÿ₁(t) + C2ÿ2(t).
C₁e² + c₂est
"
-C₁e²t + c₂e8t,
+ C2

Expert Solution

Step 1: The system of differential equation is:

$y subscript 1 superscript apostrophe equals 5 y subscript 1 plus 3 y subscript 2 y subscript 2 superscript apostrophe equals 3 y subscript 1 plus 5 y subscript 2$

With solution is

$y subscript 1 open parentheses t close parentheses equals c subscript 1 e to the power of 2 t end exponent plus c subscript 2 e to the power of 8 t end exponent y subscript 2 open parentheses t close parentheses equals negative c subscript 1 e to the power of 2 t end exponent plus c subscript 2 e to the power of 8 t end exponent$