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## Homework Statement

dL/dp = L/2, L(0) = 100. Find the solution to the differential equation, subject to the given initial condition. My textbook says the answer is L = 100e

^{p/2}, but I don't know how to get that answer (or e for that matter).

## Homework Equations

?

## The Attempt at a Solution

dL/dp = L/2

L dL/dp = 1/2

∫LdL = ∫(1/2)dp

L

^{2}/2 = x/2 + C

L

^{2}= x + 2C

(0)

^{2}= 100 + 2C

Thanks for any help ahead of time!