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).

Section 1: Theory 3 1. Theory A Bernoulli differential equation can be written in the following standard form: dy dx +P(x)y = Q(x)yn, where n 6= 1 …

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  Equations, Differential, Bernoulli, Differential equations bernoulli equations

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