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Differential Equations: An Introduction to Modern Methods and Applications
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- 1) Find all equilibrium solutions of the equation (1 − x) (x² − 4) - x = and classify each one in terms of stability. Draw a phase space diagram and sketch by hand several typical solution curves. Describe the long term (t → ±∞) behavior of the solutions.arrow_forwarddetermine the critical (equilibrium) points, and classify each one asymptotically stable, unstable, or semistable (see Problem 5). Draw the phase line, and sketch several graphs of solutions in the ty-plane. dy/dt=y2(1−y)2,−∞<y0<∞arrow_forward[14] For each of the following equations, find all equilibria; • find general solutions; • solve the initial value problem with initial condition ₁ (0) = 2, x₂(0) = 1; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. 10 x1 1 1 - 3-4 963 = (b) Q]=[4][B]+[B] x2 -5 -7 3 (a)arrow_forward
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