The equilibrium solution for the given differential equation.

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Answer 1

Question

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the given differential equation.

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

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y" +p (t)y' +q(t)y = 0 (i), can be put in more suitable form for finding a solution by making a change of the independent and/or dependent variables. Determine conditions on p and q that enable this equation to be transformed into an equation with constant coefficients by a change of the independent variable. Let r = u (t) be the new independent variable. It is easy to show (島) ( + ( +p(t) + a()y = 0 (1i). dy that dt dz dy d'y and 2 d'y d²z dy dt dz The differential equation becomes dt dr dt d'y d'z de dz dy d'y , 9 and y must be proportional. If g (t) > 0, then choose the constant of proportionality to be 1. Hence, x = u (t) = [g (t)]i dt. With a chosen this way, the coefficient of in equation (ii) is also a constant, provided that the function H = g'(t) +2p(t)q(t) is a dy In order for equation (ii) to have constant coefficients, the coefficients of constant. Thus, equation (i) can be transformed into an equation with constant coefficients by a change of the independent variable,…

I know this is False (and can explain why) but I need to provide an example to prove this.

Consider a system of differential equations describing the progress of a disease in a population, given by In our particular case, this is: a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y = x = 3-3xy - 1x y = 3xy - 2y where x (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. The y-nullclines are y = and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (x1,9₁) and (x2, y2), where we order them so that x1 < x2. The equilibrium with the smaller x-coordinate is (x₁, y₁) : The equilibrium with the larger x-coordinate is (x2, y₂) = where A = 0 sin (a) c) The linearization of the system of differential equations at the equilibrium (ï1, Y₁) gives a system of the form (+) ¹ (~), f əx ∞ a Ω = A x' G E = F(x, y) for a vector-valued function…

Answer 2

Question

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the given differential equation.

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

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Answer 3

Question

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the given differential equation.

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

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Check out a sample textbook solution

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Answer 4

Question

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the given differential equation.

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

Expert Solution & Answer

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Answer 5

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the given differential equation.

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

Answer 6

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

Answer 7

Chapter 9.2, Problem 38E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

Answer 8

b.

To determine

To sketch: The direction field for the given differential equation.

Answer 9

b.

To determine

To sketch: The direction field for the given differential equation.

Answer 10

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

Answer 11

c.

To determine

To sketch: The direction field with its given initial condition that is y(0)=1 .

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - The solution to the initial value problem y(t) = 2...

The equilibrium solution for the given differential equation.

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To Find: The equilibrium solution for the given differential equation.

To sketch: The direction field for the given differential equation.

To sketch: The direction field with its given initial condition that is y(0)=1 .

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