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ERIC Number: EJ1143734
Record Type: Journal
Publication Date: 2017
Pages: 6
Abstractor: As Provided
ISSN: ISSN-0020-739X
Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach
Tisdell, C. C.
International Journal of Mathematical Education in Science and Technology, v48 n6 p913-918 2017
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using "exact methods", illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A