Solve.
y
′
′
−
100
y
=
e
7
t
\displaystyle {y}{''}-{100}{y}={e}^{{{7}{t}}}
y
′′
−
100
y
=
e
7
t
The general solution will be
y
(
t
)
=
c
1
e
10
t
+
c
2
e
−
10
t
+
\displaystyle {y}{\left({t}\right)}={c}_{{{1}}}{e}^{{{10}{t}}}+{c}_{{{2}}}{e}^{{-{10}{t}}}+
y
(
t
)
=
c
1
e
10
t
+
c
2
e
−
10
t
+
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