Solve the separable differential equation
dxdt=x2+164,\displaystyle {\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}={x}^{{2}}+{\frac{{{1}}}{{{64}}}},
and find the particular solution satisfying the initial condition
x(0)=2.\displaystyle {x}{\left({0}\right)}=-{2}.

x(t)=\displaystyle {x}{\left({t}\right)}=   .