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Putnam
1954 Putnam
A3
A3
Part of
1954 Putnam
Problems
(1)
Putnam 1954 A3
Source: Putnam 1954
7/17/2022
Prove that if the family of integral curves of the differential equation
d
y
d
x
+
p
(
x
)
y
=
q
(
x
)
,
\frac{dy}{dx} +p(x) y= q(x),
d
x
d
y
+
p
(
x
)
y
=
q
(
x
)
,
where
p
(
x
)
q
(
x
)
≠
0
p(x) q(x) \ne 0
p
(
x
)
q
(
x
)
=
0
, is cut by the line
x
=
k
x=k
x
=
k
the tangents at the points of intersection are concurrent.
Putnam
differential equation