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.

Concepts

differential equations, solutions, graphs

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Additional Tags

math

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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

• This video is hosted on YouTube

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