1. (10 points) Find the general solution of the equation
2. (10 points) Consider the system x' =
a. Compute the fundamental matrix P(t) which satisfies P(0) = I.
b. Sketch several trajectories in the phase plane. Your sketch should note the direction
of the trajectories and indicate any asymptotic (as t too) behavior.
3. (10 points) Find the general solution to the system
and determine all initial data X0 E R³ such that the solution to the initial value problem
with x(0) = X0 remains bounded for all t 0.
4. (10 points) Solve the initial value problem
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