The general solution of the linear system x Ax is given. A-( -2 -2 X(t) =...

 

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The general solution of the linear system x Ax is given. A-( -2 -2 X(t) = c -2 -5, (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= -/2, then x(e) approaches (0, 0) along this line. Otherwise x) approaches (0, 0) from the direction determined by y = 2x. If x(0) = x, lies on the line y= 2x, then xe) approaches (0, 0) along this line. Otherwise x) approaches (0, 0) from the direction determined by y- -x/2. If x(0) - X, lies on the line y-x/2, then x(e) approaches (0, 0) along this line. Otherwise x(e) becomes unbounded and y- 2x serves as an asymptote. If x(0) = x, lies on the line y= 2x, then xe) approaches (0, 0) along this line. Otherwise x(e) becomes unbounded and y = -x/2 serves as an asymptote. All solutions spiral toward (0, 0). The general solution of the linear system x Ax is given. A-( -2 -2 X(t) = c -2 -5, (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= -/2, then x(e) approaches (0, 0) along this line. Otherwise x) approaches (0, 0) from the direction determined by y = 2x. If x(0) = x, lies on the line y= 2x, then xe) approaches (0, 0) along this line. Otherwise x) approaches (0, 0) from the direction determined by y- -x/2. If x(0) - X, lies on the line y-x/2, then x(e) approaches (0, 0) along this line. Otherwise x(e) becomes unbounded and y- 2x serves as an asymptote. If x(0) = x, lies on the line y= 2x, then xe) approaches (0, 0) along this line. Otherwise x(e) becomes unbounded and y = -x/2 serves as an asymptote. All solutions spiral toward (0, 0).