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Putnam
1997 Putnam
2
Putnam 1997 B2
Putnam 1997 B2
Source:
May 30, 2014
Putnam
function
college contests
Problem Statement
f
f
f
be a twice differentiable real valued function satisfying
f
(
x
)
+
f
′
′
(
x
)
=
−
x
g
(
x
)
f
′
(
x
)
f(x)+f^{\prime\prime}(x)=-xg(x)f^{\prime}(x)
f
(
x
)
+
f
′′
(
x
)
=
−
xg
(
x
)
f
′
(
x
)
where
g
(
x
)
≥
0
g(x)\ge 0
g
(
x
)
≥
0
for all real
x
x
x
. Show that
∣
f
(
x
)
∣
|f(x)|
∣
f
(
x
)
∣
is bounded.
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