An antibiotic is administered intravenouslyinto the bloodstream at a constant rate r. As the drug flowsthrough the patient’s system and acts on the infection that is present,it is removed from the bloodstream at a rate proportional tothe amount in the bloodstream at that time. Since the amount ofblood in the patient is constant, this means that the concentrationy = y(t) of the antibiotic in the bloodstream can be modeled bythe differential equation dy/dt = r - ky, k > 0 and constant. If y(0) = y0, find the concentration y(t) at any time t.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.