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

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

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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 $L(p) = \boxed{30e^{\frac{p}{6}}}$.

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

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