Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 10 - Differential Equations - 10.3 Euler's Method - 10.3 Exercises - Page 550: 21

Answer

The 6 values for $x_{i},y_{i}$ and for $0\leq x \leq1$ are shown in the table below
1567668334

Work Step by Step

We are given $\frac{dy}{dx}=4-y$ so that $g(x,y)=4-y$ Since $x=0, y=0$ $g(x_{0},y_{0})=4$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=0+4\times0.2=0.8$ Now $x_{1}=0.1, y_{1}=0.8$ and $g(x_{1},y_{1})=3.2$ Then $y_{2}=0.8+3.2\times0.2=1.44$ $y_{3}=1.952$ $y_{4}=2.362$ $y_{5}=2.69$ $y_{6}=2.951$
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