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
Study Strategies

Check Your Solution

Always Double-Check

After solving, plug your solution back into the original equation to ensure it works. This catches mistakes and helps you understand why your answer is correct.

Examples

  • Substitute your answer for \( y \) into the differential equation to verify both sides match.

  • Use your initial condition to check if your solution fits the starting value.