Differential equation word problem

Let x mg be the amount of drug in the patient at time t.

Drug is injected into the patient at a rate of P mg per min

The kidneys of the patient remove the drug at a rate proportional to the amount of drug at time t.

At a particular point in time, the drug concentration in the patient remains constant. This constant value is 2.5 P mg

Show that dx/dt = P - 0.4x

Hence express x in terms of P and t

In rate: P
Out rate: kx , where k is a constant

dx/dt
= In rate - Out rate
= P - kx ------- (1)

At a certain time t, x = 2.5P
In rate = Out rate
P = kx
P = 2.5Pk
k = 0.4 ------- (2)

Sub (2) into (1): dx/dt = P - 0.4x (shown)

∫ 1/(P-0.4x) dx = ∫ dt
-2.5 ln (P-0.4x) = t + c , where c is a constant

continue yourself bah, i lazy...

ok thanks ..got it :)