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Putnam
1955 Putnam
A7
Putnam 1955 A7
Putnam 1955 A7
Source:
May 23, 2022
Putnam
Problem Statement
Consider the function
f
f
f
defined by the differential equation
f
′
′
(
x
)
=
(
x
3
+
a
x
)
f
(
x
)
f'' (x) = (x^3 + ax) f(x)
f
′′
(
x
)
=
(
x
3
+
a
x
)
f
(
x
)
and the initial conditions
f
(
0
)
=
1
,
f
′
(
0
)
=
0.
f(0) = 1, f'(0) = 0.
f
(
0
)
=
1
,
f
′
(
0
)
=
0.
Prove that the roots of
f
f
f
are bounded above but unbounded below.
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