AI Tutor

Premium Lesson

Upgrade to unlock this lesson, practice questions, and your personal tutor.

This lesson is part of a track

Public learning track

Differential Equations and Mathematical Modeling

12th Grade · Math · Open Global Math

9 lessons

Goal

Formulate first-order differential equations from contextual scenarios, find general and particular solutions via separation of variables, and analyze model behavior.

9 lessons
0 of 9 done
  1. Setting Up First-Order Differential Equations from ContextUp next
  2. Solving Separable Differential Equations: General SolutionsNot started yet
  3. Finding Particular Antiderivatives Using Initial Conditions and Boundary ValuesNot started yet
  4. Modeling Exponential Growth and Radioactive DecayNot started yet
  5. Modeling Temperature Change with Newton's Law of CoolingNot started yet
  6. Modeling Population Dynamics with the Logistic Differential EquationNot started yet
  7. Modeling Kinematics with Velocity-Dependent ResistanceNot started yet
  8. Modeling Economic Supply, Demand, and Market Price DynamicsYou are here
  9. Evaluating Model Limitations and Long-Term BehaviorNot started yet
View full track

Learning standards covered

GlobalOGM.13.CAL.8Open Global Math Standards 2026™ · 12th Grade

Formulate first-order differential equations from contextual models (kinematics, population growth, Newton's law of cooling, supply-demand); solve by separation of variables to obtain general and particular solutions satisfying initial conditions, and evaluate the limitations of the model.