MTH 254 Midterm: MATH 254 Oregon State Test
31 Jan 2019
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Find all equilibrium solutions and classify them (stable, asymptotically stable, semi-stable, unstable and if system of des, node, saddle, spiral, center). For the non-linear system of des, state all possibilities for type of equilibrium solution. 1a. ) y = (y 3)(y 5)8. 1b. ) x = y 1, y = (x 3)y. The slope eld for a rst order di erential equation is shown below. In addition to determining and classifying all equilibrium solutions (if any), also draw the trajectories satisfying the initial values y(0) = 3 and y(1) = 0. The stream plot in the x1-x2 plane for a system of two rst order di erential equations is shown below. In addition to determining and classifying the 4 equilibrium solutions, also draw the trajectory satisfying the initial value (x1(0), x2(0)) = (0, 2). Also describe the basins of attraction for each asymptotically stable equilibrium solutions.
