Chem Differential Eq HW Solutions Fall 2011 202

Chem Differential - A202 Appendix A Ordinary Dierential Equations Review of Concepts and Methods We are in Case III The solutions are of the form

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

View Full Document Right Arrow Icon
A202 Appendix A Ordinary Differential Equations: Review of Concepts and Methods We are in Case III. The solutions are of the form y 1 = ± m =0 a m x m - 1 and y 2 = ky 1 ln x + ± m =0 b m x m - 2 , with a 0 ± =0 , b 0 ± = 0. Let us determine y 1 . We use y instead of y to simplify the notation. We have y = ± m =0 a m x m - 1 ; y ± = ± m =0 ( m - 1) a m x m - 2 ; y ±± = ± m =0 ( m - 1)( m - 2) a m x m - 3 . Plug into x 2 y ±± +4 xy ± +(2 - x 2 ) y : ± m =0 ( m - 1)( m - 2) a m x m - 1 + ± m =0 4( m - 1) a m x m - 1 ± m =0 2 a m x m - 1 - ± m =0 a m x m +1 ( - 1)( - 2) a 0 x - 1 + ± m =2 ( m - 1)( m - 2) a m x m - 1 +4( - 1) a 0 x - 1 + ± m =2 4( m - 1) a m x m - 1 2 a 0 x - 1 +2 a 1 + ± m =2 2 a m x m - 1 - ± m =2 a m - 2 x m - 1 2 a 1 + ± m =2 [( m - 1)( m - 2) a m +4( m - 1) a m 2 a m - a m - 2 ] x m - 1 2 a 1 + ± m =2 [( m 2 + m ) a m - a
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

Ask a homework question - tutors are online