Use undetermined coefficients to find the particular solution to
y
′
′
−
9
y
=
2
sin
(
4
t
)
\displaystyle {y}{''}-{9}{y}={2}{\sin{{\left({4}{t}\right)}}}
y
′′
−
9
y
=
2
sin
(
4
t
)
Y
(
t
)
\displaystyle {Y}{\left({t}\right)}
Y
(
t
)
=
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