Question

Find the general solution to the following linear system around the equilibrium point: x '1 =...

Find the general solution to the following linear system around the equilibrium point:

x '1 = 2x1 + x2

x '2 = −x1 + x2

(b) If the initial conditions are x1(0) = 1 and x2(0) = 1, find the exact solutions for x1 and x2.

(c) Plot the exact vector field (precise amplitude of the vector) for at least 4 points around the equilibrium, including the initial condition.

(d) Plot the solution curve starting from the initial condition x1(0) = 1 and x2(0) = 1 on the phase plane.

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