Differential Equations Help!

A = 1/30000
B = 4/30000 = 1/7500
C = -1/10000

Now we have:

(1/30000) * dP / (200 - P) + (1/7500) * dP / (P - 50) - (1/10000) * dP / P = (3/100000) * dt

Now, integrate

(-1/30000) * ln(200 - P) + (1/7500) * ln(P - 50) - (1/10000) * ln(P) = (3/100000) * t + C

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When you were explaining part B where did the -1 come from in dP/dt = (3/10) * (1/10000) * (200 - P) * (-1) * (50P - P^2)?

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and i know this will sound really stupid for asking but whats the use for integrating the function i understand how to but why would we want to? whats the resulting function do for us

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(-1/30000) * ln(200 - P) + (4/30000) * ln(P - 50) - (3/30000) * ln(P) = (3 / 100000) * t + C
(1/30000) * (4 * ln(P - 50) - ln(200 - P) - 3 * ln(P)) = (3 / 100000) * t + C
(1/3) * ln((P - 50)^4 / (P^3 * (200 - P))) = (3/10) * t + C

Now, you can solve for P. It'll be messy, but you can solve for P

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