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(Solved): For each of the differential equations below, find the critical points, draw a phase diagram, and ...



For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point det

For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) (b) (c) .


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Solution:-

a)   

Consider   

Critical points
x=0 and x=3

When flow up then    and flow down then   
For linear stability

   at   

At x=0,   
At x=-3,  

So, x=0 is stable and x=-3 is unstable



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