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Arnold's Trivium
1991 Arnold's Trivium
59
Problem 59
Problem 59
Source:
July 1, 2010
trigonometry
Problem Statement
Investigate the existence and uniqueness of the solution of the problem
y
u
x
=
x
u
y
,
u
∣
x
=
1
=
cos
y
yu_x = xu_y, u|_{x=1} =\cos y
y
u
x
=
x
u
y
,
u
∣
x
=
1
=
cos
y
in a neighbourhood of the point
(
1
,
y
0
)
(1, y_0)
(
1
,
y
0
)
.
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