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Arnold's Trivium
1991 Arnold's Trivium
63
Problem 63
Problem 63
Source:
July 1, 2010
trigonometry
Problem Statement
Is there a solution of the Cauchy problem
y
∂
u
/
∂
x
+
sin
x
∂
u
/
∂
y
=
y
y\partial u/\partial x+\sin x\partial u/\partial y=y
y
∂
u
/
∂
x
+
sin
x
∂
u
/
∂
y
=
y
,
u
∣
x
=
0
=
y
4
u|_{x=0}=y^4
u
∣
x
=
0
=
y
4
on the whole
(
x
,
y
)
(x,y)
(
x
,
y
)
plane? Is it unique?
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