To draw: The direction field for given differential equation d y d t = t 2 + y 2 with initial condition y ( 0 ) = 1 .

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Answer 1

Question

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

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Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

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Answer 2

Question

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Expert Solution & Answer

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Answer 5

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Answer 6

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

Answer 7

Chapter 8.3, Problem 14P

(a)

To determine

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

Answer 8

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

Answer 9

(b)

To determine

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

Answer 10

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Answer 11

(c)

To determine

To obtain: An accurate approximation to the solution at t=1.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 8.1 - Prob. 1P Ch. 8.1 - In each of Problems 1 through 6, find approximate...Ch. 8.1 - In each of Problems 1 through 6, find approximate...Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.1 - Prob. 10P

To draw: The direction field for given differential equation d y d t = t 2 + y 2 with initial condition y ( 0 ) = 1 .

To draw: The direction field for given differential equation dydt=t2+y2 with initial condition y(0)=1.

The approximate values of the solution at given initial value by Runge-Kutta method with h=0.0125.

To obtain: An accurate approximation to the solution at t=1.

Want to see the full answer?

Chapter 8 Solutions