Lecture 19

# Lecture 19 - Section 4.6 cont’d Section 4.7 Variation of...

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Unformatted text preview: Section 4.6, cont’d, Section 4.7 Variation of Parameters/Variable Coefficients April 8, 2009 Variation of Parameters/Variable Coefficients Today’s Session A Summary of This Session: (1) Justification of Variation of Parameters. (2) Variable-Coefficient Equations (Euler’s Method). Variation of Parameters/Variable Coefficients Variation of Parameters Suppose you want to find a particular solution to the constant coefficient differential equation ay ′′ + by ′ + cy = f ( t ) Find the fundamental solutions of the homogeneous equation y 1 and y 2 . Find a particular solution of the form y p = v 1 ( t ) y 1 ( t ) + v 2 ( t ) y 2 ( t ) by solving the system braceleftBig v ′ 1 y 1 + v ′ 2 y 2 = v ′ 1 y ′ 1 + v ′ 2 y ′ 2 = f ( t ) a Variation of Parameters/Variable Coefficients Variation of Parameters The answers are given by: v ′ 1 =- f ( t ) y 2 a W ( y 1 , y 2 ) and v ′ 2 = f ( t ) y 1 a W ( y 1 , y 2 ) Or v 1 =- integraldisplay f ( t ) y 2 a W ( y 1 , y 2 ) and v 2 = integraldisplay...
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## This note was uploaded on 10/06/2009 for the course MATH 254 taught by Professor Indik during the Spring '08 term at Arizona.

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Lecture 19 - Section 4.6 cont’d Section 4.7 Variation of...

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