Differential Equations

Study of equations involving derivatives and their applications.

What are Differential Equations?First-Order Differential EquationsInitial Value Problems
Second-Order Differential EquationsSystems of Differential EquationsPartial Differential Equations (PDEs)
Modeling Population GrowthPhysics: Motion and ForcesMedicine: Drug Dosage and Decay
Break Down the ProblemCheck Your Solution
What are Differentia...First-Order Differen...Initial Value Proble...Second-Order Differe...Systems of Different...Partial Differential...Modeling Population ...Physics: Motion and ...Medicine: Drug Dosag...Break Down the Probl...Check Your Solution
Practical Applications

Medicine: Drug Dosage and Decay

Keeping Medicine Levels Safe

Doctors use differential equations to predict how quickly a drug leaves your body and how much should be given to keep you healthy.

The Equation

\( \frac{dC}{dt} = -kC \), where \( C \) is the concentration and \( k \) is a constant.

Why Does This Matter?

It ensures medicine is effective without being dangerous.

Examples

  • Determining how often to take a painkiller.

  • Calculating safe levels for anesthesia during surgery.

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