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Expert-verified Found in: Page 271 ### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069 # In Problems 15–18, find all critical points for the given system. Then use a software package to sketch the direction field in the phase plane and from this description the stability of the critical points (i.e., compare with Figure 5.12).

This is unstable saddle point is (-2,1).

See the step by step solution

## Step 1: Find critical points

Here the system is;

$\frac{dx}{dt}=2x+y+3\phantom{\rule{0ex}{0ex}}\frac{dy}{dt}=-3x-2y-4$

For critical points equate the system equal to zero.

$2x+y+3=0\phantom{\rule{0ex}{0ex}}-3x-2y-4=0$

Solve for x and y by eliminating the method.

The values of x=-2 and y=1.

So, this is the unstable saddle point is (-2,1).

## Step 2: Sketch This is the required result.

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