Create a phase portrait for dy dx = y² (25 - y²) and classify each equilibrium solution.
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- Find the equilibria solutions Plot the phase lineFor each equilibrium solution, determine if it is asymptotically stable, semistable or unstable.Find all equilibrium solutions (with steps) and classify is stable, semistable, or unstable.Solve and identify the type of equilibrium point at the origin. x' 3 5.
- For the Attached problem, Identify the equilibrium values. Which are stable and which are unstable? Construct a phase line. Identify the signs of and Sketch several solution curvesFor each equation draw a phase line (label the axis) labeling all critical points and their stability. dy =-y' +3y -2y dt dx b. =x*(3-x) dt a.Find the equilibrium solutions and analyze the stability using the phase diagram.
- The survival of two species depends on their mutual cooperation. For instance, a species of bee that feeds primarily on the nectar of one plant species and simultaneously pollinates the plant. One simple model of mutualism is given by dx/xt = −ax + bxydy/dt = −my + nxy where a, b, m, and n are all positive constants. Perform a graphical analysis and indicate the trajectory directions in the phase plane.find sol. y'- y =y2e-xAnalyze the dynamics of the system x' = y, y' = -x(1x) + cy for different positive values of c. Draw phase diagrams for each case, illustrating the behavior.
- For the phase portrait shown below 1 -1 -2 -3 -4 -5 Classify the equilibrium point (0,0). Give type, and indicate whether it is stable or unstable.Consider the autonomous system y' = y (y – 3) (a) Write a phase portrait for the above equation. (b) Identify any stable equilibrium solutions. (c) Identify any unstable equilibrium solutions.Obtain the phase plane of the system x´= 1 - x2y´ = xy Solve for y=y(x). Please be as clear and legible as possible. Show all the steps. Thank you.