This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y h ( x ) = c 1 xe x + c 2 e x . Combining this with the particular solution, y p ( x ) = x 2 e x , we Fnd that a general solution is given by y ( x ) = y p ( x ) + y h ( x ) = x 2 e x + c 1 xe x + c 2 e x . 9. We can write the nonhomogeneous term as a dierence t 2 + 4 t t 2 e t sin t = ( t 2 + 4 t ) ( t 2 e t sin t ) = g 1 ( t ) g 2 ( t ) . Both, g 1 ( t ) and g 2 ( t ), have a form suitable for the method of undetermined coecients. Therefore, we can apply this method to Fnd particular solutions y p, 1 ( t ) and y p, 2 ( t ) to 3 y + 2 y + 8 y = g 1 ( t ) a n d 3 y + 2 y + 8 y = g 2 ( t ) , respectively. Then, by the superposition principle, y p ( t ) = y p, 1 ( t ) y p, 2 ( t ) is a particular solution to the given equation. 197...
View
Full
Document
This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

Click to edit the document details