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In each of 9 and 10, let 0(t) = 0 and use the method of

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 9 Chapter 2.8

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 9

In each of 9 and 10, let 0(t) = 0 and use the method of successive approximationsto approximate the solution of the given initial value problem.(a) Calculate 1(t), ... , 3(t).(b) Plot 1(t), ... , 3(t) and observe whether the iterates appear to be converging.y= t2 + y2, y(0) = 0

Step-by-Step Solution:
Step 1 of 3

S343 Section 2.7 Notes- Euler’s Method of Numerical Approximation 9-13-16  Used for equations that cannot be solved without computer- give numerical approximation of at given values  Known as first-order method/tangent line method- error at each step (iteration) decreases like ℎ decreases +ℎ − )  Recall = (, )) = ℎ→0 ( ℎ ) where ℎ = uniform step size between and +1 (ie. = + ℎ) +1 +ℎ −() o (, )) ≈ ℎ  ℎ( (, ))≈ + ℎ − ( ) 

Step 2 of 3

Chapter 2.8, Problem 9 is Solved
Step 3 of 3

Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

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In each of 9 and 10, let 0(t) = 0 and use the method of