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1-002-IntegratingFactor-TechniqueNarrative

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: Integrating Factor

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Abstract

Resource Image We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Principles of How People Learn

Description

We then have to face the other side of our modified differential equation and this still could be difficult or impossible to antidifferentiate.

Despite this, the method works for a number of differential equations which are reasonable models of phenomena.

Basically we build a function (called an integrating factor) with which we multiply both sides of our differential equation we wish to solve so that one side looks just like the derivative of a product of two functions.

This makes one side of the differential equation easy to anti-differentiate, but we have to address the other side of the differential equation which we just multiplied by the integrating factor.

There are modeling situations which lead to such equations and we use one involving electrical circuits to motivate the method.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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