Answered: Solve the following differential…

Solve the following differential system: 2 1(0) with -3 y(0). Hint. One eigenvalue and its corresponding eigenvector of A are r = -2+i, u, = -1+i

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 15CR

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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)
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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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