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4.12 Variational calculus
Problem: Find the extremals of the functional:
I
[
y
(
x
)
]
=
∫
−
1
1
y
(
1
+
y
2
)
d
x
,
y
(
0
)
=
1
2
,
y
(
1
)
=
1
2
.
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