266_pdfsam_math 54 differential equation solutions odd

# 266_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

Chapter 5 Thus, a general solution to the given system is u ( t )= c 1 1 2 c 2 e t + 1 2 e t + 5 3 t, v ( t c 1 + c 2 e t + 5 3 t. 9. Expressed in operator notation, this system becomes ( D +2)[ x ]+ D [ y ]=0 , ( D 1)[ x ]+( D 1)[ y ]=s i n t. In order to eliminate the function y ( t ), we will apply the operator ( D 1) to the Frst equation above and the operator D to the second one. Thus, we have ( D 1)( D x D 1) D [ y ]=( D 1)[0] = 0 , D ( D 1)[ x ] D ( D 1)[ y ]= D [sin t cos t. Adding these two equations yields the di±erential equation involving the single function x ( t ) given by ± ( D 2 + D 2) ( D 2 D ) ² [ x cos t 2( D 1)[ x cos t. (5.3) This is a linear Frst order di±erential equation with constant coeﬃcients and so can be solved by the methods of Chapter 2. (See Section 2.3.) However, we will use the methods of
This is the end of the preview. Sign up to access the rest of the 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.

Ask a homework question - tutors are online