Method of Undetermined Coefficients

Method of Undetermined Coefficients - Differential...

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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 133 Lesson 27 The Method of Undetermined Coefficients Specific Objectives: At the end of the lesson, the students are expected to: differentiate the different methods on the determination of the particular solution solve non homogeneous equations using different methods A non-homogeneous linear differential equation with constant coefficients is of the form: ( ) ( ) + + + + + = 1 2 0 1 2 1 ... n n n n n a D a D a D a D a y R x To find its general solution, y = y c + y p . The complementary solution, y c , may be determined from the roots of the auxiliary equation, f(m) = 0, and the particular solution, y p , may be determined by: The particular solution may be found by any of the following methods: 1. The Method of Undetermined Coefficients 2. Variation of Parameters 3. Inverse Operators 4. By Inspection 1. The Method of Undetermined Coefficients This method may be used if R(x) is itself a solution of some homogeneous linear differential equation with constant coefficients . Step 1. Consider the right hand side of the equation, R(x) and determine its roots. Case 1. If there is no repetition of roots between the auxiliary equation and R(x) such that when R(x) is a then y P is a. constant like 2, 3, etc. A b. linear function like 3x, 2x + 5, etc. Ax + B
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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna
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Method of Undetermined Coefficients - Differential...

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