Solve the following differential system:¤(0)y(0)2with3Hint. One eigenvalue and its corresponding eigenvector of A are r = -2+i, uį =r(t)24 costaeThen you obtain-2e 4(cost + sin t)Please type in a :

Consider the equation as shown below: Here,xy = -12-1-3xy with x0y0 = 4-2 And the object is to find…

Answered: Solve the following differential…

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

Solve the following differential system:
¤(0)
y(0)
2
with
3
Hint. One eigenvalue and its corresponding eigenvector of A are r = -2+i, uį =
r(t)
24 cost
ae
Then you obtain
-2e 4(cost + sin t)
Please type in a :

Expert Solution

Step 1

Consider the equation as shown below:

Here, $(\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} - 1 & 2 \\ - 1 & - 3 \end{matrix}) (\begin{matrix} x \\ y \end{matrix})$ with $(\begin{matrix} x (0) \\ y (0) \end{matrix}) = (\begin{matrix} 4 \\ - 2 \end{matrix})$

And the object is to find the solution of the $x (t)$ and $y (t)$ .

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