Differential Equation

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SECOND-ORDER DIFFERENTIAL EQUATIONS

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Presentation transcript:

Differential Equation Chapter 4 Non Homogeneous Differential Equation 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 The general solution of the non - homogeneous differential equation There are two parts of the solution: 1. solution of the homogeneous part of DE 2. particular solution General Solution 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 General solution Particular Solution Complementary Function, solution of Homgeneous part Due to f(x) 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 This method can be applied to any non-homogeneous differential equation no matter What the coefficients and the function f(x) are. Method of undetermined coefficients is mostly quicker and easier to apply as it involves differentiation. Whereas method of variation of parameters involve Integration. We may prefer to use method of undetermined coefficients where ever possible. 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 To apply method of variation of parameters STEP: 1. Step:2. Identify Step:3. 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4

Method of Variation of Parameters Chapter 4 4/14/2017 Method of Variation of Parameters Chapter 4