For this linear system:dx/(dt)=x+y−2 dy/(dt)=x−y−4 Classify (1,1)

Trystan Castaneda 2022-08-13 Answered
For this linear system:
d x d t = x + y 2
d y d t = x y 4
Classify ( 1 , 1 )
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Answers (1)

cydostwng6c
Answered 2022-08-14 Author has 13 answers
d y d x = d y d t d x d t = x y 4 x + y 2
At ( 1 , 1 ) , d y d x 0, ( 1 , 1 ) , d y d x 0. Indeed, at ( 1 , 1 ), d y d x is not defined.
d y d x = 0 when x y 4 = 0
But this doesn't tell us too much: only that x y = 4. (Two variables and one equation. Infinitely many solutions.)
On the other hand, if you find the Jacobian and evaluate the eigenvalues, you'll find that your critical point is ( 3 , 1 ), and is a saddle point.
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