Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach
| Autor: | Christopher Tisdell, Johnny Henderson |
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| Rok vydání: | 2016 |
| Předmět: |
Bernoulli differential equation
Differential equation 020209 energy Applied Mathematics 05 social sciences First-order partial differential equation 050301 education Exact differential equation 02 engineering and technology Education Integrating factor Examples of differential equations Mathematics (miscellaneous) Ordinary differential equation 0202 electrical engineering electronic engineering information engineering Calculus Riccati equation 0503 education Mathematics |
| Zdroj: | International Journal of Mathematical Education in Science and Technology. 48:913-918 |
| ISSN: | 1464-5211 0020-739X |
| DOI: | 10.1080/0020739x.2016.1272143 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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