For the system
x’ = x
y’ = −y;
a. Sketch the vector field in the phase plane.
b. Write down the differential equation for the trajectories (giving dy=dx as a function of x and y), and
solve it to find the trajectories. Sketch the trajectories in the phase plane.
c. Find the general solution of the system, giving x and y as functions of t. Check that your solutions
satisfy the equations of the trajectories found in part b.
d. What type of equilibrium point does this system have? Is it stable or unstable?
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