Consider the system of differential equations dxdt 04x 05y

Consider the system of differential equations dx/dt = 0.4x + 0.5y, dy/dt = 1.5x - 0.6y. 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) = 7, y(0) = 6 is x(t) = y(t) =

Solution

Post multiple questions to get the remaining answers and specify the file pplane9.m

[x\',y\'] = [0.4 0.5; 1.5 - 0.6] [x,y]

You need to find the eigen value such that det(A-lambda*I) = 0

Det(A) = 0

(0.4-p)(-0.6-p) - 0.75 = 0

(p-0.4)(p+0.6) - 0.75 = 0

p^2 + 0.2p - 0.24 - 0.75 = 0

p^2 + 0.2p - 0.99 = 0

p1 = 0.9 and p2 = -1.1

Hence the smaller eigen value is equal to -1.1 and the larger eigen value is 0.9

0.4 - p	0.5
1.5	-0.6 - p