Solve the separable differential equation

dxdt=3x,\displaystyle \frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}=\frac{{3}}{{x}},

and find the particular solution satisfying the initial condition x(0)=4.\displaystyle {x}{\left({0}\right)}={4}.

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