In Problems 19–24, convert the given second-order equation into a first-order system by setting v=y’. Then find all the critical points in the yv-plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12).
The point is an unstable saddle point (0, 0).
Here the equation is .
Then the given system can be written as:
For critical points equate the system equal to zero.
So, the critical point is (0, 0).
The phase plane equation is:
This is the required result.
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