Modeling Medication Concentration Using Power Series Solutions

You’re taking a new medication and want to understand how its concentration changes in your bloodstream over time. After taking a dose, your body both absorbs the medication into your bloodstream and gradually eliminates it through your liver and kidneys. The concentration [latex]y(t)[/latex] of the medication (in milligrams per liter) at time [latex]t[/latex] hours after taking the dose satisfies the differential equation [latex]y'' - y = 0[/latex]. This equation captures the balance between absorption and elimination processes in your body. Using power series methods, you can model exactly how the medication concentration changes, helping you understand when the medication is most effective and how long it stays in your system.