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Putnam
1951 Putnam
B1
B1
Part of
1951 Putnam
Problems
(1)
Putnam 1951 B1
Source:
5/25/2022
Find the conditions that the functions
M
(
x
,
y
)
M(x, y)
M
(
x
,
y
)
and
N
(
x
,
y
)
N (x, y)
N
(
x
,
y
)
must satisfy in order that the differential equation
M
d
x
+
N
d
y
=
0
Mdx + Ndy =0
M
d
x
+
N
d
y
=
0
shall have an integrating factor of the form
f
(
x
y
)
.
f(xy).
f
(
x
y
)
.
You may assume that
M
M
M
and
N
N
N
have continuous partial derivatives of all orders.
Putnam