Question: Can I have some help with this Exercise 1. For each of the following autonomous differential equations y' = f(y) perform each of the following

Can I have some help with this

Can I have some help with this Exercise 1. For each of

Exercise 1. For each of the following autonomous differential equations y' = f(y) perform each of the following tasks. (i) Determine the equilibrium points and sketch a graph of f(y). (ii) Construct the phase line and classify each equilibrium point as either unstable or asymptot ically stable. (iii) Sketch the equilibrium solutions in the ty-plane. These equilibrium solutions divide the ty-plane into regions. Sketch at least one solution curve in each of these regions. (iv) Predict the limiting behavior of the solution to the initial value problem y' = f(y), y(to) = yo depending on the initial value yo. (1) y' = -y? + 4y -3; Exercise 2. Check that the following differential forms are exact and find the solutions to the corresponding initial value problems. (1) (3thy - 2t) dt + (+3 + 6y - y?) dy = 0, y(0) = 3. Exercise 3. For each of the following, show that the differential form is not exact, but becomes exact when multiplied through by the given integrating factor u(t, y). Then find the general solution to the differential form equation. (1) el dt + (e cot(y) + 2 y sin(y) dy =0, u(t, y) = sin(y)

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