Differential Equations

Study of equations involving derivatives and their applications.

What Are Differential Equations?First-Order Differential EquationsSecond-Order Differential Equations
Systems of Differential EquationsPartial Differential EquationsNonlinear Differential Equations and Chaos
Modeling Population GrowthEngineering Vibrations and OscillationsMedical and Biological Applications
How to Approach Differential Equation ProblemsTips for Test Day Success
What Are Differentia...First-Order Differen...Second-Order Differe...Systems of Different...Partial Differential...Nonlinear Differenti...Modeling Population ...Engineering Vibratio...Medical and Biologic...How to Approach Diff...Tips for Test Day Su...
Study Strategies

How to Approach Differential Equation Problems

Step-by-Step Problem Solving

  1. Identify the type of equation: Is it first-order, second-order, linear, or nonlinear?
  2. Look for clues: Are there any obvious substitutions or simplifications?
  3. Pick a method: Try separation of variables, integrating factors, or characteristic equations.
  4. Check solutions: Substitute your answer back into the original equation to see if it works.

Stay Calm and Organize

Draw diagrams, write out each step, and don't be afraid to try more than one method if you get stuck!

Examples

  • Spotting a separable equation and solving by integrating both sides.

  • Trying an integrating factor when you see a linear first-order equation.

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Tips for Test Day Success