Use separation of variables to find the solution to the differential equation $\frac{d L}{d p}=\frac{L}{6}$ if $L(0)=30$. \[ L(p)= \]

Step 1 ：This is a first order linear differential equation. The general solution to such an equation is given by the formula \(L(p) = Ce^{kp}\), where C is a constant and k is the coefficient of L in the differential equation. In this case, k = 1/6.

Step 2 ：We also know that \(L(0) = 30\), which allows us to solve for C.

Step 3 ：Substituting the values into the equation, we get \(L = 30*exp(p/6)\).

Step 4 ：The solution to the differential equation is \(L(p) = \boxed{30e^{\frac{p}{6}}}\).