Homework-6-f10_Sol

Homework-6-f10_Sol - AMS 361 Applied Calculus IV by Prof Y...

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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 ...
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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.

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