Use undetermined coefficients to find the particular solution to
y
′
′
+
7
y
′
+
12
y
=
2
sin
(
t
)
\displaystyle {y}{''}+{7}{y}'+{12}{y}={2}{\sin{{\left({t}\right)}}}
y
′′
+
7
y
′
+
12
y
=
2
sin
(
t
)
Y
(
t
)
\displaystyle {Y}{\left({t}\right)}
Y
(
t
)
=
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