5. Consider the linear system below. x ‘ = x y ‘ = x + 2 y a. Write this system in vector form….

5.          Consider the linear system below.

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5. Consider the linear system below. x ‘ = x y ‘ = x + 2 y a. Write this system in vector form….
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x' = x

y' = x + 2y

 

a.          Write this system in vector form.

 

b.          Since the system can be decoupled, first find the solution of x' = x

and then use that to find the solution of y' = x + 2y.

 

c.           Write this solution in vector form.

 

d.          Do the 2 above solutions generate the general solution?

 

e.           Sketch the above solutions in the phase plane.