By Inspection - Silva, Alviso and Llacuna – Mathematics...

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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 155 Lesson 30 By Inspection &on-Homogeneous Equation 4. Inspection It is easy to obtain a particular solution of a non–homogeneous linear differential equation by inspection if R(x) is a constant, R 0 . Standard Form: ( ) ( ) + + + + + = 1 2 0 1 2 1 ... n n n n n a D a D a D a D a y R x Case I. if n o p n a R y then a = , 0 Case II. if k n k o p n a k x R y then a = = ! , 0 Where: R 0 = constant found on the right side of the equation a n = constant term a n–k = coefficient of the lowest–ordered derivative k = lowest–ordered derivative Example: Find the particular solution of the differential equation. 2 5 5 , 2 5 ) 2 .( 2 3 4 12 12 , 4 12 ) 4 .( 1 2 2 = = = = = = = = = + p o n p p p o n p y R a y D D y y R a y D
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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________
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Unformatted text preview: Silva, Alviso and Llacuna – Mathematics Department, MIT 156 3 3 3 3 3 5 2 3 54 81 ) 9 )( 3 )( 2 )( 1 ( 81 ) 9 ( ! 3 81 9 , 3 , 81 , 81 ) 9 .( 3 x y x y x y x y a K R a y D D p p p p k n o n p − = − = − = − = − = = = = = − − x y x y x y a K R a y D D D p p p k n o n p 10 ) 2 ( 1 20 ) 2 ( ! 1 20 2 , 1 , 20 , 20 ) 2 .( 4 1 2 3 − = − = − = − = = = = = − + − Seatwork: Find the particular solution of the differential equation. 1. (D 2 – 2D + 8) y p = 16 2. (D 3 + D 2 – 2D) y p = 20 Homework: Find the particular solution of the differential equation. 1. (D 2 – 9D - 3) y p = 27 2. (D 4 – 2D 3 - 5D 2 + 6D) y p = 15...
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This note was uploaded on 01/17/2012 for the course MATH 24 taught by Professor Dantesilva during the Spring '11 term at Mapúa Institute of Technology.

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By Inspection - Silva, Alviso and Llacuna – Mathematics...

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