Q15E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

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).

Step-by-Step Solution

Answer

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

Step 1: Find critical points

Here the system is;

 $$\begin{gathered} \frac{dx}{dt}=2x+y+3 \\ \frac{dy}{dt}=-3x-2y-4 \end{gathered}$$

 

For critical points equate the system equal to zero.

$$\begin{gathered} 2x+y+3=0 \\ -3x-2y-4=0 \end{gathered}$$ 

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.