Program Explanation Given information: Differential equation is written below. y ′ = − 2 x y , y ( 0 ) = 2 The value of x 0 , y 0 , and f ( x , y ) are written below. x 0 = 0 y 0 = 2 f ( x , y ) = − 2 x y The actual solution of the differential equation is y ( x ) = 2 e − x 2 . The interval is [ 0 , 1 2 ] and step size is 0.25 for first time and 0.1 for second time. h 1 = 0.25 h 2 = 0.1 Explanation: Apply the Euler method with step size h 1 = 0.25 in the interval [ 0 , 1 2 ] with initial value ( x 0 , y 0 ) ≡ ( 0 , 2 ) as follows: The number of terms needed is calculated as, n = b − a h 1 = 0.5 − 0 0.25 = 2 Obtain the value of y 1 as, y 1 = y 0 + h 1 ( − 2 x 0 y 0 ) = 2 + 0.25 ( − 2 ( 0 ) ( 2 ) ) = 2 Obtain the value of y 2 as, y 2 = y 1 + h 1 ( − 2 x 1 y 1 ) = 2 + 0.25 ( − 2 ( 0.25 ) ( 2 ) ) = 1.75 Therefore, the value of y ( 1 2 ) is 1.75 for step size h 1 = 0.25 . Similarly, apply the Euler method with step size h 2 = 0.1 in the interval [ 0 , 1 2 ] with initial value ( x 0 , y 0 ) ≡ ( 0 , 2 ) as follows: The number of terms needed is calculated as, n = b − a h 2 = 0

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ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 2.4, Problem 6P

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Program Description: Purpose of the problem is to obtain the value of y(12) by the use of Euler method with step size 0.25 and 0.1, also compare with the value y(12) of the actual solution.

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Chapter 2.4, Problem 5P

Chapter 2.4, Problem 7P

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Chapter 2 Solutions

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Program Description: Purpose of the problem is to obtain the value of y ( 1 2 ) by the use of Euler method with step size 0.25 and 0.1, also compare with the value y ( 1 2 ) of the actual solution.

Solution Summary: The author explains how to obtain the value of y(12) by the use of Euler method with step size 0.25 and 0.1, and compare with the actual solution.

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Program Description: Purpose of the problem is to obtain the value of y(12) by the use of Euler method with step size 0.25 and 0.1, also compare with the value y(12) of the actual solution.

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Chapter 2 Solutions