Math Is Fun Forum

I may have messed up on the way so here is the full problem...

"The drug is removed by the patient's kidneys a rate which is proportional to the concentration of the drug in the patients blood..."

From this i thought...Rate Out = k * conc. of drug

and conc. of drug is r/v1 where r (as above) is the mg of drug in the blood and v1 is the constant ammount of blood in the body

so Rate Out = k * r/v1 ...is this the right thinking?

and dr/dt = Rate in - Rate out...using the rate out k*r/v1 and the rate in given in the question below

Rest of question...

"Derive a differential equation describing the dependence on time of the drug concentration in the patient's blood. You can assume the volume of the patient's blood is a constant and that the rate of drug addition per unit volume of blood is a1 + a2*sin(k1*t) where a1, a2 and k1 are constants and t is time."

The rest of the questions gives values and asks to plug them in etc which is straight forward...just stuck on integrating the diff. equation and whether or not I even have the correct diff. equation in the first place...