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: 4


$y(0.6) \approx 0.0603$

Work Step by Step

We are given $\frac{dy}{dx}=x+y^{2}$ so that $g(x,y)=x+y^{2}$ Since $x=0, y=0$ $g(x_{0},y_{0})=0$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=0+0\times0.1=0$ Now $x_{1}=0.1, y_{1}=0$ and $g(x_{1},y_{1})=0.1+0^{2}=0.1$ Then $y_{2}=0+0.1\times0.1=0.01$ $y_{3}=0+(0.2001)\times0.1=0.02001$ $y_{4}=0+(0.3004)\times0.1=0.03004$ $y_{5}=0+(0.4009)\times0.1=0.04009$ $y_{6}=0+(0.5016)\times0.1=0.05016$ $y_{7}=0+(0.6025)\times0.1=0.06025$ $y(0.6)$ mean $x=0.6 \rightarrow y_{7}=0.06025 \approx 0.0603$
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