Differential Equations and Initial Value Problems

Demonstrate working an initial value problem with an AP Calculus video that verifies that a family of functions is a solution to a differential equation by substitution. The presentation goes on to find a particular solution that belongs to a given initial value.

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Instructional Ideas
  • Use a graphing program to graph several members of the family of solutions
  • Provide opportunities for pupils to verify solutions of an equation
Classroom Considerations
  • The class should know how to differentiate a function
Pros
  • Uses a graphical representation of the particular solution
  • After making a mistake, the presenter talks through the process to find his mistake — great for pupils to see
Cons
  • None