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Lecture 2.1: Separation of Variables Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 2080, Differential Equations M. Macauley (Clemson) Lecture 2.1: Separation of Variables

  1. Lecture 2.1: Separation of Variables Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 2080, Differential Equations M. Macauley (Clemson) Lecture 2.1: Separation of Variables Math 2080, ODEs 1 / 5

  2. Introduction Definition The order of an ODE is the highest derivative that appears. Example 1 (exponential growth) Find all solutions to y ′ = ky . M. Macauley (Clemson) Lecture 2.1: Separation of Variables Math 2080, ODEs 2 / 5

  3. Exponential decay Example 2 Find all solutions to y ′ = − ky . M. Macauley (Clemson) Lecture 2.1: Separation of Variables Math 2080, ODEs 3 / 5

  4. Exponential growth vs. decay M. Macauley (Clemson) Lecture 2.1: Separation of Variables Math 2080, ODEs 4 / 5

  5. Decay to a limiting value Example 3 Find all solutions to y ′ = k (72 − y ). M. Macauley (Clemson) Lecture 2.1: Separation of Variables Math 2080, ODEs 5 / 5

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