09934 01148 ℎ 09934 01148 input output g ty y1 3y2

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InputOutput>>g = @(t,Y) [Y(1) + 3*Y(2); -Y(1) - 8*Y(2)];P = [-3,3; -3,0; -3,2; -2,-3; -1,3; 0,-3; 1,4; 2,-3; 4,-2; 4,0; 4,2];phaseplane(g, [-4.5,4.5], [-4.5,4.5], 16)hold onfor i=1:size(P,1)drawphase(g, 50, P(i,1), P(i,2))endhold offComment: Plot matches my prediction above.-4-3-2-101234-4-3-2-101234
Exercise 4.3:Consider the system of differential equations(6)dxdt= 2.7x - ydydt= 4.1x + 3.7ya.Put the system above in the form=Avand enter the matrixA =into MATLAB. UseMATLAB to find the eigenvalues and eigenvectors ofA =. Copy and paste all input andoutput from your command into your Word document.b.Write the general solution of the system (6) in your Word document.c.Use phaseplane and drawphase to create a phase diagram of the solution. Make sure todraw at least six different curves using drawphase. Include the resulting plot in yourwriteup. Which feature of the eigenvalues or eigenvectors causes the solutions to tendto infinity astgrows large?

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