To determine The y -values of solution for the given x and Δ x . Explanation Formula used: The approximate solution to a differential equation of the form d y d x = f ( x , y ) , that passes through a known point ( x 0 , y 0 ) is obtained by the Runge-Kutta method. According to the Runge Kutta Method the next point of ( x n , y n ) is obtained using the formula y n + 1 = y n + 1 6 ( K 1 + 2 K 2 + 2 K 3 + K 4 ) and x n + 1 = x n + h . where: K 1 = h f ( x n , y n ) K 2 = h f ( x n + h 2 , y n + K 1 2 ) K 3 = h f ( x n + h 2 , y n + K 2 2 ) K 4 = h f ( x n + h 2 , y n + K 3 2 ) Calculation: For n = 1 the value of h = 0.1 , ( x 1 , y 1 ) = ( 0 , 0 ) . Then the value of K 1 is calculated as: K 1 = h f ( 0 , 0 ) = 0.1 ( 0 × 0 + 1 ) = 0.1 The value of K 2 is calculated as follows. K 2 = h f ( x 1 + h 2 , y 1 + K 1 2 ) = 0

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 31.5, Problem 9E

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The y-values of solution for the given x and Δx.

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Chapter 31.5, Problem 8E

Chapter 31.5, Problem 10E

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Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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