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Putnam
1957 Putnam
B6
Putnam 1957 B6
Putnam 1957 B6
Source: Putnam 1957
July 1, 2022
Putnam
analytic geometry
graphing lines
differential equation
Problem Statement
The curve
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
satisfies
y
′
(
0
)
=
1.
y'(0)=1.
y
′
(
0
)
=
1.
It satisfies the differential equation
(
x
2
+
9
)
y
′
′
+
(
x
2
+
4
)
y
=
0.
(x^2 +9)y'' +(x^2 +4)y=0.
(
x
2
+
9
)
y
′′
+
(
x
2
+
4
)
y
=
0.
Show that it crosses the
x
x
x
-axis between
x
=
3
2
π
and
x
=
63
53
π
.
x= \frac{3}{2} \pi \;\;\; \text{and} \;\;\; x= \sqrt{\frac{63}{53}} \pi.
x
=
2
3
π
and
x
=
53
63
π
.
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