Transcription of Differential Equations BERNOULLI EQUATIONS - …
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Differential Equations BERNOULLI EQUATIONS - …
Differential EquationsBERNOULLI EQUATIONSG raham S McDonaldA Tutorial Module for learning how to solveBernoulli differential equationslTable of contentslBegin Tutorialc of factor on using solutionsFull worked solutionsSection 1: Theory31. TheoryABernoulli differential equationcan be written in the followingstandard form:dydx+P(x)y=Q(x)yn,wheren6= 1 (the equation is thusnonlinear).To find the solution, change the dependent variable fromytoz, wherez=y1 n. This gives a differential equation inxandzthat islinear, and can be solved using the integrating factor : Dividing the above standard form byyngives:1yndydx+P(x)y1 n=Q(x) (1 n)dzdx+P(x)z=Q(x)(where we have useddzdx= (1 n)y ndydx).TocJJIIJIBackSection 2: Exercises42. ExercisesClick onExerciselinks for full worked solutions (there are 9exercises in total) exercise general form of a BERNOULLI equation isdydx+P(x)y=Q(x)yn,wherePandQare functions ofx, andnis a constant.
Section 2: Exercises 4 2. Exercises Click on Exercise links for full worked solutions (there are 9 exercises in total) Exercise 1. The general form of a Bernoulli equation is
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