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Putnam
1956 Putnam
B1
Putnam 1956 B1
Putnam 1956 B1
Source: Putnam 1956
July 5, 2022
Putnam
differential equation
Problem Statement
Show that if the differential equation
M
(
x
,
y
)
d
x
+
N
(
x
,
y
)
d
y
=
0
M(x,y)\, dx +N(x,y) \, dy =0
M
(
x
,
y
)
d
x
+
N
(
x
,
y
)
d
y
=
0
is both homogeneous and exact, then the solution
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
satisfies that
x
M
(
x
,
y
)
+
y
N
(
x
,
y
)
xM(x,y)+yN(x,y)
x
M
(
x
,
y
)
+
y
N
(
x
,
y
)
is constant.
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