Consider the system of differential equations dx/dt = -1.6x + 0.5y, dy/dt +2.5x

Question

Consider the system of differential equations dx/dt = -1.6x + 0.5y, dy/dt +2.5x - 3.6y. For this system, the smaller eigenvalue is and the larger eigenvalue is Use the phase plotter pplane9.m in MATLAB to determine how the solution curves behave. The solution curves converge to different points. All of the solution curves converge towards 0. (Stable node) The solution curves race towards zero and then veer away towards infinity. (Saddle).All of the solution curves run away from 0. (Unstable node) The solution to the above differential equation with initial values x(0) = 3, y(0) = 7 is x(t) = y(t) =

Explanation / Answer

when we will try to find eigenvalues we will get lambda

=-1,1   and = -4.1 and all the curve converge   towards 0

it means B

for last part we have

U:

Singular Value Decomposition:

S:

VT

Eigenvectors:

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