Ordinary Differential Equations/First Order

First Order Differential Equations

The simplest types of differential equations to solve are the first order equations. These are equations where the highest derivative in the equation is the first. So, a first order equation is a function $F(x,y,y^{\prime })$; there are no occurrences of $y^{\prime \prime }$ or higher derivatives.

There are two easily solved types of first order equations. These are equations with separable variables and linear equations. This chapter covers how to solve and graph any equation in one of these forms, or reducible to these forms. Other types of differential equations, such as non-linear equations, are not covered yet.

2: Separable First Order Differential Equations

• [[../Separable 1|Explanation]]
• [[../Separable 2|Examples]]
• [[../Separable 3|Problems]]
• [[../Separable 4|Answers]]

4: First Order Linear Differential Equations

• [[../First Order Linear 1|Explanation]]
• [[../First Order Linear 2|Examples]]
• [[../First Order Linear 3|Problems]]
• [[../First Order Linear 4|Answers]]

1: Exact Differential Equations

• [[../Exact 1|Explanation]]
• [[../Exact 2|Examples]]
• [[../Exact 3|Problems]]
• [[../Exact 4|Answers]]

3: Substitution Methods

• [[../Substitution 1|Explanation]]
• [[../Substitution 2|Examples]]
• [[../Substitution 3|Problems]]
• [[../Substitution 4|Answers]]

===5: Graphing Differential Equations

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• [[../Graphing 1|Slope Fields]]
• [[../Isoclines 1|Isoclines]]

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