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Miklós Schweitzer
1961 Miklós Schweitzer
7
Miklós Schweitzer 1961- Problem 7
Miklós Schweitzer 1961- Problem 7
Source:
December 1, 2015
college contests
Problem Statement
7. For the differential equation
∂
2
u
∂
x
2
+
∂
2
u
∂
y
2
=
2
∂
2
u
∂
x
∂
y
\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}= 2\frac{\partial^2 u}{\partial x \partial y}
∂
x
2
∂
2
u
+
∂
y
2
∂
2
u
=
2
∂
x
∂
y
∂
2
u
find all solutions of the form
u
(
x
,
y
)
=
f
(
x
)
g
(
y
)
u(x,y)=f(x)g(y)
u
(
x
,
y
)
=
f
(
x
)
g
(
y
)
. (R. 14)
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