Find the particular solution to a differential equation whose general solution and initial condition are given. ( $C$ is the constant of integration.) \[ x(t)=C e^{3 t}, x(0)=7 \] \[ x(t)= \]

Step 1 ：The general solution of the differential equation is given by \(x(t)=C e^{3 t}\).

Step 2 ：We are also given an initial condition \(x(0)=7\).

Step 3 ：We can use this initial condition to find the value of the constant \(C\).

Step 4 ：Substituting \(t=0\) into the general solution gives \(x(0) = C e^{3*0} = C\).

Step 5 ：Setting this equal to the initial condition gives \(C = 7\).

Step 6 ：Now that we have found the value of the constant \(C\) to be 7, we can substitute this value back into the general solution to find the particular solution.

Step 7 ：The particular solution to the differential equation is \(x(t)=7 e^{3 t}\).

Step 8 ：Final Answer: The particular solution to the differential equation is \(\boxed{7 e^{3 t}}\).