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Arnold's Trivium
1991 Arnold's Trivium
60
Problem 60
Problem 60
Source:
July 1, 2010
calculus
integration
Problem Statement
Is there a solution of the Cauchy problem
x
(
x
2
+
y
2
)
∂
u
∂
x
+
y
3
∂
u
∂
y
=
0
,
u
∣
y
=
0
=
1
x(x^2+y^2)\frac{\partial u}{\partial x}+y^3\frac{\partial u}{\partial y}=0,\;u|_{y=0}=1
x
(
x
2
+
y
2
)
∂
x
∂
u
+
y
3
∂
y
∂
u
=
0
,
u
∣
y
=
0
=
1
in a neighbourhood of the point
(
x
0
,
0
)
(x_0,0)
(
x
0
,
0
)
of the
x
x
x
-axis? Is it unique?
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