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Differential Equations - Notes
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## First Order Differential Equations

In this chapter we will look at solving first order differential equations. The most general first order differential equation can be written as,

 (1)

As we will see in this chapter there is no general formula for the solution to (1). What we will do instead is look at several special cases and see how to solve those. We will also look at some of the theory behind first order differential equations as well as some applications of first order differential equations. Below is a list of the topics discussed in this chapter.

Linear Equations  Identifying and solving linear first order differential equations.

Separable Equations  Identifying and solving separable first order differential equations.  We’ll also start looking at finding the interval of validity from the solution to a differential equation.

Exact Equations  Identifying and solving exact differential equations.  We’ll do a few more interval of validity problems here as well.

Bernoulli Differential Equations  In this section we’ll see how to solve the Bernoulli Differential Equation.  This section will also introduce the idea of using a substitution to help us solve differential equations.

Substitutions  We’ll pick up where the last section left off and take a look at a couple of other substitutions that can be used to solve some differential equations that we couldn’t otherwise solve.

Intervals of Validity  Here we will give an in-depth look at intervals of validity as well as an answer to the existence and uniqueness question for first order differential equations.

Modeling with First Order Differential Equations  Using first order differential equations to model physical situations.  The section will show some very real applications of first order differential equations.

Equilibrium Solutions  We will look at the behavior of equilibrium solutions and autonomous differential equations.

Euler’s Method  In this section we’ll take a brief look at a method for approximating solutions to differential equations.

 Final Thoughts Previous Section Next Section Linear Equations Basic Concepts Previous Chapter Next Chapter Second Order DE's

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