2. DS: phase-plane, equilibria a. Identify each phase portrait below with a vector field from the following list: F=(y,-sinx); G ={(1-x-y/2)x,(1– y-2x/3) y}; H =(y,x-x'). Assign fields (F,G,H) to appropriate models: VL-competition, Duffing oscillator, pendulum. In each case explain the meaning of variables (x,y) and coefficients b. Sketch null-clines, and find all equilibria on each plot, describe equilibria types. 2.0 1.0 0.6 -2

Q: a direction field for d = 2t+y². Use the direction field to sketch a solution cu on y(0) = -1.

A: To draw the direction field of the DE , let first find the equilibrium points.(There is a misprint…

Q: Let r(t) = 5e7t + e2t and y(t) = 3e2t + 1le (i) Rewrite the given functions in the vector form Y(t)…

A:

Q: 6. Consider the system x' = 2r y=-y. I (a) Sketch the vector field. (b) Show that for every solution…

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Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

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Q: Subtracting the two equations, find a vector equation for the curve of 3 intersection between y =…

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A: The given vector valued function

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A: We’ll answer the first part of this question since due to complexity. Please submit the question…

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Q: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: b) Plot the vector fields for different values of h (show all qualitative behaviors)

A: The given equation is, dxdτ=x1-x-h So, the vector field for different values of h are as follows.