Determine the nature and stability of the critical point (0,0) for the following system: dx/dt =x+2y+2 sin y dy/dt =-3y-xe^x

skilpadw3 2022-07-27 Answered
Determine the nature and stability of the critical point (0,0) for the following system:
d x d t = x + 2 y + 2 sin y
d y d t = 3 y x e x
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Answers (1)

Jeroronryca
Answered 2022-07-28 Author has 13 answers
The equilibrium solutions (or points) to a system of first order differential equations are the points at which the first derivatives are equal to zero.
That is, for the system:
dx/dt = f(x,y)
dy/dt = g(x,y),
the equilibrium points are the solutions to the algebraic equations:
f(x,y) = 0
g(x,y) = 0
Now = 0
x + 2 y + 2 sin y = 0
and =0
Therefore 3 y x e x = 0
From these two we observe that the critical point is (0,0)
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