Consider the system of differential equations dx/dt= x+ y=1
dy/dt =1- x^2 +y^2

Required:
Sketch the x-nullcline, where solutions must travel vertically. Identify the regions in the plane where solutions will move toward the right, and where solutions move toward the right.

Step-by-step explanation:

Given that:

the differential equations:

For x-nullcline;

From the image attached below, the sketch of the x-nullcline was carefully drawn and the regions were identified.

So, x-increases at the time when

Thus, the solution move towards the right for  x+y>1

step-by-step explanation:

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