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IberoAmerican Olympiad For University Students
1998 IberoAmerican Olympiad For University Students
6
6
Part of
1998 IberoAmerican Olympiad For University Students
Problems
(1)
Differential equation implies bounded - OIMU 1998 Problem 6
Source:
9/12/2010
Take the following differential equation:
3
(
3
+
x
2
)
d
x
d
t
=
2
(
1
+
x
2
)
2
e
−
t
2
3(3+x^2)\frac{dx}{dt}=2(1+x^2)^2e^{-t^2}
3
(
3
+
x
2
)
d
t
d
x
=
2
(
1
+
x
2
)
2
e
−
t
2
If
x
(
0
)
≤
1
x(0)\leq 1
x
(
0
)
≤
1
, prove that there exists
M
>
0
M>0
M
>
0
such that
∣
x
(
t
)
∣
<
M
|x(t)|<M
∣
x
(
t
)
∣
<
M
for all
t
≥
0
t\geq 0
t
≥
0
.
integration
calculus
derivative
limit
real analysis
IberoAmerica Undergrad MO
1998 IberoAmerica Undergrad MO