1. Differential Equations
Chapter 10
Differential Equations
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Chapter Outline
Solutions of Differential Equations
Separation of Variables
First-Order Linear Differential Equations
Applications of First-Order Linear Differential Equations
Graphing Solutions of Differential Equations
Applications of Differential Equations
Numerical Solution of Differential Equations
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3. First-Order Linear Differential Equations
Section 10.3
First-Order Linear
Differential Equations
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First-Order Linear Differential Equations
Definition
Example
A first-order linear differential equation is a differential equation in the form of
where a(t) and b(t) are continuous function on a given interval.
A solution for a linear differential equation using chain rule and product rule
is as follows:
where eA(t) is called an integrating factor.
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General Steps for Solving a First-Order Linear DE
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Solve a First-Order Linear DE
EXAMPLE
SOLUTION
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Solve a First-Order Linear DE
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Solve an Initial Value Problem
EXAMPLE
SOLUTION
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Solve an Initial Value Problem
Continued
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