Question
Asked Oct 28, 2019
y(x) for which the integral
Stationary Path Find the path y
1.
X2
I/1-y2(x)dx
X1
is stationary.
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y(x) for which the integral Stationary Path Find the path y 1. X2 I/1-y2(x)dx X1 is stationary.

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Step 1

For the path to be stationary, the Euler-Lagrange equation must be:

af
d af
= 0
y dx Oy
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af d af = 0 y dx Oy

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Step 2

Here, the function f is:

f -y(x)
х.
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f -y(x) х.

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Step 3

Now, as the function f is independent ...

af
= constant
oy'
k
ôy'
o(x-y (x)
= k
1
(0-2y'(x))k
(1-y2(x))
2
xy'(x)
-k
(1-y2(x))
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af = constant oy' k ôy' o(x-y (x) = k 1 (0-2y'(x))k (1-y2(x)) 2 xy'(x) -k (1-y2(x))

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