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: 5


$y(0.6)= y_{7}=1.1676$

Work Step by Step

We are given $\frac{dy}{dx}=x+\sqrt y$ so that $g(x,y)=x+\sqrt y$ Since $x=0, y=1$ $g(x_{0},y_{0})=1$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=1+1\times0.1=1.1$ Now $x_{1}=0.1, y_{1}=1.1$ and $g(x_{1},y_{1})=1.149$ Then $y_{2}=1+1.149\times0.1=1.115$ $y_{3}=1+(1.256)\times0.1=1.1256$ $y_{4}=1+(1.361)\times0.1=1.1361$ $y_{5}=1+(1.466)\times0.1=1.1466$ $y_{6}=1+(1.571)\times0.1=1.1571$ $y_{7}=1+(1.676)\times0.1=1.1676$ $y(0.6)= y_{7}=1.1676$
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