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Mathematics
Problem
Let
u
(
t
)
u(t)
u
(
t
)
and
v
(
t
)
v(t)
v
(
t
)
satisfy the system
d
u
d
t
=
−
5
v
\dfrac{du}{dt}=-5v
d
t
d
u
=
−
5
v
and
d
v
d
t
=
5
u
\dfrac{dv}{dt}=5u
d
t
d
v
=
5
u
. Derive a second-order differential equation that involves
u
u
u
only (eliminate
v
v
v
).
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