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Arnold's Trivium
1991 Arnold's Trivium
20
20
Part of
1991 Arnold's Trivium
Problems
(1)
Problem 20
Source:
7/1/2010
Find the derivative of the solution of the equation
x
¨
=
x
+
A
x
˙
2
\ddot{x} =x + A\dot{x}^2
x
¨
=
x
+
A
x
˙
2
, with initial conditions
x
(
0
)
=
1
x(0) = 1
x
(
0
)
=
1
,
x
˙
(
0
)
=
0
\dot{x}(0) = 0
x
˙
(
0
)
=
0
, with respect to the parameter
A
A
A
for
A
=
0
A = 0
A
=
0
.
calculus
derivative
parameterization
function
inequalities