(a) find the eigenvalues; (b) determine if the origin is a spiral sink, a spiral

Question

(a) find the eigenvalues;

(b) determine if the origin is a spiral sink, a spiral source, or a center;

(c) determine the natural period and natural frequency of the oscillations,

(d) determine the direction of the oscillations in the phase plane (do the solutions go

clockwise or counterclockwise around the origin?); and

(e) sketch the xy-phase portrait and the x(t)- and y(t)-

graphs for the solutions with the indicated initial conditions.

Y/Dt = ( 1 4)

-3 2

Y, with initial condition Y0 = (1,−1)

Explanation / Answer

some wierd symbols are being displayed please recheck and no matrix is given for which eigen values have to be determined

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