Determine the nature and stability of thecritical point (0,0) for the following system: dx/dt =-sin (x-y) dy/dt =1-5y -e^x

Nathalie Fields 2022-07-24 Answered
Determine the nature and stability of thecritical point (0,0) for the following system:
d x d t = sin ( x y )
d y d t = 1 5 y e x
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Answers (1)

dominicsheq8
Answered 2022-07-25 Author has 15 answers
The equilibrium solutions (or points) to a system of first order differential equations are the points at which the first derivatives are equalto 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
= 0
This implies that x y = 0 x = y
=0
Then the above Equation becomes
1 5 x e x = 0
e x = 1 5 x
when x = 0 both L.H.S and R.H.S are Equal
Therefore x = 0 and y = 0
Therefore the critical point is (0,0)
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