2. Given the system 1 10 X'=(- ¹2) X 1 (a) Write the general solution. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories.

Consider the following system of differential equations describing two populations: æ' = 0.02a (1 – ) + 0.004xy 80 (1 y' = 0.04y(1 ) - 0.0002xy 20 a. Describe what the equations tell us about the populations (how the populations behave absent interaction, and how interaction affects each population). b. Find all equilibrium points algebraically. c. Classify each equilibrium using linearization d. Sketch some solution curves in the phase plane (x-y plane)

State the general form of a particular solution to y" + 3y' – y = 3te-24. (Do not solve for the constants associated with the particular solution.)

Solve and identify the type of equilibrium point at the origin. x' 3 5.