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Unformatted text preview: GE 207K Homogeneous Equations September 14, 2010 This page aims to recap our mini-lecture on homogenous equations. A differential equation which can be written in the form y = g y x . In other words, the differential equation can be written such that anywhere the dependant variable appears, it appears as fraction y x . These equations can be turned into separable equations by performing a substitution. These homogenous equations are different than the class of differential equations which we classified as homogenous on the first day. The following steps can be taken to find the general solution to the differential equation: Steps: 1. Write the given differential equation in the right form. y = g y x (1) 2. Eliminate y from the differential equation entirely by rewriting the differential equation in terms of x and (a newly introduced variable) u . Do this by performing the following substitutions: (a) Perform the substitution in the differential equation u = y x . (2) (b) Replace y with the following expression...
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- Fall '10