25_pdfsam_math 54 differential equation solutions odd

25_pdfsam_math 54 differential equation solutions odd - y =...

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

View Full Document Right Arrow Icon
Exercises 1.4 ( x n ,y n )w i th( x n +1 ,y n +1 ), n =0 , 1 ,..., 9. Since f ( x, y )= x 2 yx 1 y 2 , the recursive formulas have the form x n +1 = x n +0 . 1 , y n +1 = y n +0 . 1 ± 1 x 2 n y n x n y 2 n ² ,n =0 , 1 ,..., 9 , x 0 =1 , y 0 = 1. Therefore, x 1 =1+ 0 . 1=1 . 1 ,y 1 = 1+0 . 1 ± 1 1 2 1 1 ( 1) 2 ² = 0 . 9; x 2 =1 . 1+0 . 1=1 . 2 ,y 2 = 0 . 9+0 . 1 ± 1 1 . 1 2 0 . 9 1 . 1 ( 0 . 9) 2 ² ≈− 0 . 81653719 ; x 3 =1 . 2+0 . 1=1 . 3 ,y 3 = 0 . 81653719 + 0 . 1 ± 1 1 . 2 2 0 . 81653719 1 . 2 ( 0 . 81653719) 2 ² ≈− 0 . 74572128 ; x 4 =1 . 3+0 . 1=1 . 4 ,y 4 = 0 . 74572128 + 0 . 1 ± 1 1 . 3 2 0 . 74572128 1 . 3 ( 0 . 74572128) 2 ² ≈− 0 . 68479653 ; etc . The results of these computations (rounded to Fve decimal places) are shown in Table 1-B. Table 1–B : Euler’s method approximations for the solutions of y 0
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y = x 2 yx 1 y 2 , y (1) = 1, on [1 , 2] with h = 0 . 1. n x n y n n x n y n 1.0 1 . 00000 6 1.6 . 58511 1 1.1 . 90000 7 1.7 . 54371 2 1.2 . 81654 8 1.8 . 50669 3 1.3 . 74572 9 1.9 . 47335 4 1.4 . 68480 10 2.0 . 44314 5 1.5 . 63176 The function y ( x ) = 1 /x = x 1 , obviously, satisFes the initial condition, y (1) = 1. urther 21...
View Full Document

Ask a homework question - tutors are online