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Please show the work so I learn Determine the coefficients p, q, and the determi

ID: 1813374 • Letter: P

Question

  Please show the work so I learn  

Determine the coefficients p, q, and the determinant (delta) of the system:
                 y1'=y1 + 10y2
                 Y'2=7y1 - 8y2
                 Based on these values, what is the type and stability of the critical point?


                 a.)   p=-9, q=9, delta =16, Stable and Node
                 b.)   p=0,q=78, delta =361, Stable and Saddle point
                 c.)   p=-7,q, q= -78, delta = 361, Unstable and node
                 d.)   p=10, q=9, delta =64, Stable and Saddle point
                 e.)   None of the above; see Problem Work

Determine the eigenvalues of the system: y1'=8y1-y2 y'2=y1+10y2 What is the stability of the critical point? lambda(base)1=2+i2,lambda= 2-i2, Stable lambda (base)1,lambda(base)2=9, Unstable lambda(base)1=-9+i2,lambda=-9-i2, Stable lambda(base)1=2+i2, lambda=2-i2, Stable and attractive None of the above; see Problem Work

Explanation / Answer

matrix A =

[1   10]

[7    -8]


|y*I - A| = 0


==>


|y-1   -10|

|-7    y+8| = 0


==>


(y-1)(y+8) - 70 = 0


==>


y^2 + 7y - 78 = 0


==>


y = 6, -13


Real, opposite sign: saddle point (unstable)


e.)   None of the above;