Explanation 1) Concept: Euler’s Method Approximate values for the solution of the initial-value problem y ' = F ( x , y ) , y x 0 = y 0 , with step size h , at x n = x n - 1 + h are y n = y n - 1 + h F x n - 1 , y n - 1 w h e r e n = 1 , 2 , 3 , … 2) Given: The initial value problem y ' = cos ⁡ x + y , y 0 = 0 The step sizes h = 0.2 3) Calculation: Given that the initial value problem y ' = cos ⁡ x + y , y 0 = 0 So, we use Euler’s method with y ' = cos ⁡ x + y , & y 0 = 0 This gives, x 0 = 0 , y 0 = 0 Step size h = 0.2 Using these in y n = y n - 1 + h F x n - 1 , y n - 1 We get y 1 = y 0 + h F ( x 0 , y 0 ) y 1 = 0 + 0

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Author: James Stewart

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Chapter 9.2, Problem 24E

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Euler’s method with step size 0.2 to estimate y(0.6) the solution of given initial value problem.

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Chapter 9.2, Problem 23E

Chapter 9.2, Problem 25E

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To use: Euler’s method with step size 0.2 to estimate y ( 0.6 ) the solution of given initial value problem.

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Euler’s method with step size 0.2 to estimate y(0.6) the solution of given initial value problem.

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To use: Euler’s method with step size 0.2 to estimate y ( 0.6 ) the solution of given initial value problem.

Solution Summary: The author uses Euler's method with step size 0.2 to estimate the solution of the initial-value problem.

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To use: Euler’s method with step size 0.2 to estimate y(0.6) the solution of given initial value problem.

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Chapter 9 Solutions

To use:

Euler’s method with step size 0.2 to estimate y(0.6) the solution of given initial value problem.