Solve the separable differential equation
d
x
d
t
=
x
2
+
1
64
,
\displaystyle {\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}={x}^{{2}}+{\frac{{{1}}}{{{64}}}},
d
t
d
x
=
x
2
+
64
1
,
and find the particular solution satisfying the initial condition
x
(
0
)
=
−
2.
\displaystyle {x}{\left({0}\right)}=-{2}.
x
(
0
)
=
−
2
.
x
(
t
)
=
\displaystyle {x}{\left({t}\right)}=
x
(
t
)
=
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