Differential Equations

Basic DE's and Separable Equations

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Session Overview

In this session we will introduce our most important differential equation and its solution: y’ = ky. This DE models exponential growth or decay. We will also learn how to solve what are called separable equations. Finally, we will see first-order linear models of several physical processes.

Session Activities

Read the course notes:

• The Most Important DE (PDF)
• Other Basic Examples (PDF)
• Separation of Variables (PDF)

Check Yourself

Take the quizzes:

• Separation of Variables (PDF)
• Choices (PDF)
• Answer (PDF)
• Is it Separable? (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Solutions that Blow Up: The Domain of a Solution (PDF)
• Modeling by First Order Linear ODE’s (PDF)

Learn from the Mathlet materials:

• Watch the video Introduction to the 18.03 Applets
• Work with the Amplitude and Phase: First Order Applet

Watch the problem solving video:

• Separable Equations

Complete the practice problem:

• Practice Problem (PDF)
• Solution (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I (PDF)
• Problem Set Part I Solutions (PDF)
• Problem Set Part II (PDF)
• Problem Set Part II Solutions (PDF)

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