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he general solution of the linear system X' = AX is given. 4 cos(4t) sin(4t) ) -4 sin(4t) +C, A = X(t) = e cos(4t) (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -4x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x/4. O If X(0) = X, lies on the line y = -x/4, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -4x. O If X(0) = X, lies on the line y = -x/4, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -4x serves as an asymptote. O If X(0) = X, lies on the line y = -4x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x/4 serves as an asymptote. O All solutions spiral toward (0, 0).

he general solution of the linear system X' = AX is given. 4 cos(4t) sin(4t) ) -4 sin(4t) +C, A = X(t) = e cos(4t) (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -4x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x/4. O If X(0) = X, lies on the line y = -x/4, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -4x. O If X(0) = X, lies on the line y = -x/4, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -4x serves as an asymptote. O If X(0) = X, lies on the line y = -4x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x/4 serves as an asymptote. O All solutions spiral toward (0, 0).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The general solution of the linear system X' = AX is given. 4 cos(4t) -4 sin(4t) cos(4t), A = X(t) = e + sin(4t) (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -4x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x/4. O If X(0) = X, lies on the line y = -x/4, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -4x. O If X(0) = X, lies on the line y = -x/4, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -4x serves as an asymptote. O If X(0) = X, lies on the line y = -4x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x/4 serves as an asymptote. All solutions spiral toward (o, 0).
Transcribed Image Text:The general solution of the linear system X' = AX is given. 4 cos(4t) -4 sin(4t) cos(4t), A = X(t) = e + sin(4t) (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O If X(0) = X, lies on the line y = -4x, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -x/4. O If X(0) = X, lies on the line y = -x/4, then X(t) approaches (0, 0) along this line. Otherwise X(t) approaches (0, 0) from the direction determined by y = -4x. O If X(0) = X, lies on the line y = -x/4, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -4x serves as an asymptote. O If X(0) = X, lies on the line y = -4x, then X(t) becomes unbounded along this line. Otherwise X(t) becomes unbounded and y = -x/4 serves as an asymptote. All solutions spiral toward (o, 0).
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