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Calculus / Fundamentals of Differential Equations 8 / Chapter 3.6 / Problem 1E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

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Chapter 3, Problem 1E

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QUESTION:

many of the following problems, it will be essential to have a calculator or computer available. You may use a software package† or write a program for solving initial value problems using the improved Euler’s method algorithms on pages 127 and 128. (Remember, all trigonometric calculations are done in radians.) Show that when Euler’s method is used to approximate the solution of the initial value problem at x = 1, then the approximation with step size h is (1 + 5h)1/h

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QUESTION:

many of the following problems, it will be essential to have a calculator or computer available. You may use a software package† or write a program for solving initial value problems using the improved Euler’s method algorithms on pages 127 and 128. (Remember, all trigonometric calculations are done in radians.) Show that when Euler’s method is used to approximate the solution of the initial value problem at x = 1, then the approximation with step size h is (1 + 5h)1/h

ANSWER:

SolutionStep 1 of 4We have to solve the given initial value problem with Euler’s method and then show that The approximate solution of the given differential equation at is with step size h is

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