Use undetermined coefficients to find the particular solution to
y
′
′
+
y
′
+
2
y
=
3
t
2
+
5
t
+
9
\displaystyle {y}{''}+{y}'+{2}{y}={3}{t}^{{2}}+{5}{t}+{9}
y
′′
+
y
′
+
2
y
=
3
t
2
+
5
t
+
9
y
p
(
t
)
\displaystyle {y}_{{p}}{\left({t}\right)}
y
p
(
t
)
=
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