The general solution of the linear system X' = AX is given. -3 3 A-(13-))--(-:)*+,().-44 :. -2 -3 X(t) 1 = et + e 1 3 e1

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The General Solution Of The Linear System X Ax Is Given 3 3 A 13 44 2 3 X T 1 Et E 1 3 E1 1 (56.21 KiB) Viewed 17 times

The general solution of the linear system X' = AX is given. -3 3 A-(13-))--(-:)*+,().-44 :. -2 -3 X(t) 1 = et + e 1 3 e110 e (a) In this case discuss the nature of the solution in a neighborhood of (0,0). If X(0) = x, lies on the line y = -x/3, then X(t) approaches (0,0) along this line. Otherwise X(t) approaches (0,0) from the direction determined by y = 3x. If X(0) = x, lies on the line y = 3x, then X(t) approaches (0,0) along this line. Otherwise X(t) approaches (0,0) from the direction determined by y = -x/3. If X(0) = X, lies on the line y = -x/3, then X(t) approaches (0,0) along this line. Otherwise X(t) becomes unbounded and y = 3x serves as an asymptote. If X(0) = X, lies on the line y = 3x, then X(t) approaches (0,0) along this line. Otherwise X(t) becomes unbounded and y = -x/3 serves as an asymptote. O All solutions spiral toward (0,0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(O) = (1, 1). y y у y у (1, 1) (1, 1) (1, 1) (1, 1) 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 X X X X - 1.0 -0.5 0.5 1.0 - 1.0 -0.5 0.5 1.0 - 1.0 -0.5 0.5 1.0 - 1.0 -0.5 0.5 1.0 -0.5 -0.5 -0.5 -0.5 - 1.0 - 1.0 - 1.0 - 1.0 O