solve the ode & graph the phase plane The image displays a system of differential equations:\[\begin{cases} \dot{x} = -5x + 2y \\ \dot{y} = x - 6y \end{cases}\]This system describes the rates of change of two variables, $ x $ and $ y $, with respect to time. The equations are commonly found in mathematical modeling contexts, such as in the analysis of dynamic systems in engineering or the natural sciences.

We have given system of DE'sIt can be written asLet, called as coefficients matrix.

Answered: (x=-5x+2y j y = x-6y

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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solve the ode & graph the phase plane

The image displays a system of differential equations:

\[
\begin{cases}
\dot{x} = -5x + 2y \\
\dot{y} = x - 6y
\end{cases}
\]

This system describes the rates of change of two variables, $ x $ and $ y $, with respect to time. The equations are commonly found in mathematical modeling contexts, such as in the analysis of dynamic systems in engineering or the natural sciences.

Expert Solution

Step 1: Description of given data

We have given system of DE's

$x apostrophe equals negative 5 x plus 2 y y apostrophe equals x minus 6 y$

It can be written as

$open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets equals open square brackets table row cell negative 5 x plus 2 y end cell row cell x minus 6 y end cell end table close square brackets$

$open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets equals open square brackets table row cell negative 5 end cell 2 row 1 cell negative 6 end cell end table close square brackets open square brackets table row x row y end table close square brackets$

Let, $A equals open square brackets table row cell negative 5 end cell 2 row 1 cell negative 6 end cell end table close square brackets$ called as coefficients matrix.