Advanced Engineering Mathematics
Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 6.3, Problem 1E
To determine

The analytic solution of the initial value problem y=x+y1,y(0)=1 and compare the actual values y(0.2), y(0.4), y(0.6) and y(0.8) with approximate values in example 1.

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(b) Let I[y] be a functional of y(x) defined by [[y] = √(x²y' + 2xyy' + 2xy + y²) dr, subject to boundary conditions y(0) = 0, y(1) = 1. State the Euler-Lagrange equation for finding extreme values of I [y] for this prob- lem. Explain why the function y(x) = x is an extremal, and for this function, show that I = 2. Without doing further calculations, give the values of I for the functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
L sin 2x (1+ cos 3x) dx 59
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