Alternate solution to generalised Bernoulli equations via an integrating factor: An Exact Approach

New mathematical / pedagogical research http://dx.doi.org/10.1080/0020739X.20... Enjoy!!
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 generalised Bernoulli equation, constructing a general solution by linearising the problem through a substitution.

The purpose of this note is to present an alternative approach using ``exact methods", illustrating that a substitution and linearisation 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.

Please Cite As:
Tisdell, CC, 2017, Alternate solution to generalized Bernoulli equations
via an integrating factor: an exact differential equation approach. International Journal of Mathematical Education in Science and Technology, Volume 48, Issue 6, pages 813-918.
http://dx.doi.org/10.1080/0020739X.20...