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Chapter 9: Q17E (page 425)

Question:Consider the system

dx鈫�dt=[位100位2]x鈫�.

For the values of and given in Exercises 16 through 19, sketch the trajectories for all nine initial values shown in the following figure. For each of the points, trace out both the future and the past of the system.

17.位1=1,位2=2

Short Answer

Expert verified

Answer

The trajectories for all nine initial values is

Step by step solution

01

Draw the future and past of the system.

Consider the Eigen values 位1=1and位2=2.

As , 位2>位1>0the future and past of the system toward outside.

Draw the graph of E1andE2as follows.

02

Draw the trajectory of the system.

If the Eigen values of the system are 位1=1and位2=2such that 位2>位1>0then the phase portraits of the system is

By the definition of trajectory, draw the graph of the trajectory of the system as follows.

Hence, the trajectories for all nine initial values and trace of future and past of the system is sketched.

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