Unformatted text preview: AMS 361: Applied Calculus IV by Prof Y. Deng
Homework 6
Assignment Date: Collection Date:
Grade: Thursday (10/28/2010) Thursday (11/04/2010)
Each problem is worth 10 points. Problem 6.1 Find the general solution of the following equation ( )(
( )(
)( )( )()
) √ √ ( (√ ) (√ )) () Problem 6.2 Find the general solution of the following equation (
Substitute () The original equation becomes ) () ( The characteristic equation is ( ) ) () () () ( () ( ( )) ( ( )) ) () () 1 Problem 6.3 Compute the following Vandermonde determinant       ( ( ) )
) ( ( (
) )  )
  ( ( ) ) ( ( ) )  ( )( ( ( ) ) ∏( ∏( ) ) ( ( ) ) ( ( ) ( )  )(  ) ( ) ( ) ∏( ) Problem 6.4 Find the general solution for the following equation, ( ) ( ) () Let () () () () () () () () 2 ( () ( )) ( () () () () )( ( () () ) ( )) () () ( )( ( ) ) This becomes () () ( ( )) Thus, () () ∫ ( ) ( ) () () () ( ) Problem 6.5 Find the particular solution for (with constants ( ) ) Characteristic Equation ( For the articular solution, ()   ∫ ( )∫ ( ) (  () () ) ( ( ) ) ∫ ( ( ( () () )∫ ( ) ( ) )  ) ) ( ) Problem 6.6 Find the particular solution for 3 Characteristic Equation () () Particular Equation Since i and 1 are simple roots and ( ) ( () () () ( ( )) () ( ( )) ) ( () ( ) ( ) ( ) ) () () ( () ( )) ( )) () ( ) () () ( () ) ( ) ( ) () ( ) () () ( ( ) ) ( ) ( ) () () ( ) ( ) 4 () () () () ( ) ( ) 5 ...
View
Full
Document
This note was uploaded on 01/31/2011 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Staff

Click to edit the document details