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Differential Equations

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Single Trajectory of an Autonomous Differential Equation

DIFFEQ-LCLYEA

Which of the following sets CANNOT represent a single trajectory of an autonomous differential equation ${\bf x}'={\bf f}({\bf x})$, where ${\bf f}:{\mathbb R}^2\rightarrow {\mathbb R}^2$ and ${\mathbb R}^2$ represents the plane?

A

Choice 'A' is shown in figure.

B

Choice 'B' is shown in figure.

C

Choice 'C' is shown in figure.

D

Choice 'D' is shown in figure.