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dx/dt = -x^2 -xy + 4x dy/dt = -2y^2 -xy + 3y A) Find the nullclines and use them

ID: 2830981 • Letter: D

Question

dx/dt = -x^2 -xy + 4x

dy/dt = -2y^2 -xy + 3y

A) Find the nullclines and use them to find the equilibrium solutions ?

B) Linearize the only equilibrim solution in the first quadrant to classify it ?

C) Draw the phase portrait ?

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Q2) Find the general solution of the system :

d^2y/dt^2 + 3 dy/dt + 5y = diracdelta4 (t) ,

y(0)=2 and y'(0) =1

Explanation / Answer

A) The x-nullcline are given by dx/dt=0 => x=0 or -x-y+4=0

The y-nullcline are given by dy/dt=0 => y=0 or -2y-x+3=0

Clearly the points of intersection between x-nullcline and y-nullcline are exactly the equilibrium points.