Program Description: Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation d x d t = 1 10 x ( 10 − x ) − h and then construct the bifurcation diagram. Summary introduction: Problem will use the separation of the variable for differential equation d y d x = f ( x ) g ( y ) and the integral of x − 1 can be calculated as ∫ 1 x d x = ln | x | + c where c is called the constant of integration.

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Answer 1

Question

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

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3. (i) Using the definition of the line integral of a vector field, calculate the line integral L³ F.dy of the vector field F: R² → R² given by F(x, y) = (y, x), and where the curve & is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]

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Answer 2

Question

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

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Answer 3

Question

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

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Answer 4

Question

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

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Answer 5

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

Answer 6

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

Answer 7

Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter h of the differential equation dxdt=110x(10−x)−h and then construct the bifurcation diagram.

Summary introduction:

Problem will use the separation of the variable for differential equation dydx=f(x)g(y) and the integral of x−1 can be calculated as ∫1xdx=ln|x|+c where c is called the constant of integration.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

Solution Summary: The author explains that the problem is to calculate the dependence of the number of critical points on the parameter h of a differential equation.

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Chapter 2 Solutions