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Problems
Mathematics
Mathematics
Problem
If
y
=
e
−
x
cos
x
y=e^{-x}\cos x
y
=
e
−
x
cos
x
and
y
n
+
k
n
y
=
0
y_n+k_n y=0
y
n
+
k
n
y
=
0
, where
y
n
=
d
n
y
d
x
n
y_n=\frac{d^n y}{dx^n}
y
n
=
d
x
n
d
n
y
and
k
n
k_n
k
n
are constants
∀
n
∈
N
\forall n\in N
∀
n
∈
N
, then (a)
k
4
=
4
k_4=4
k
4
=
4
(b)
k
8
=
−
16
k_8=-16
k
8
=
−
16
(c)
k
12
=
20
k_{12}=20
k
12
=
20
(d)
k
16
=
−
24
k_{16}=-24
k
16
=
−
24
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