# 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 *+ 2*y*

* *

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 *+ 2*y*.

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.