Repeat Exercise 3(a) and (b) using the extrapolation discussed in Example 2. In exercise 3(a) and (b) a. y = 3y' + 2y + 2x

Repeat Exercise 3(a) and (b) using the extrapolation discussed in Example 2.
In exercise 3(a) and (b)
a. y" = ˆ’3y' + 2y + 2x + 3, 0 ‰¤ x ‰¤ 1, y(0) = 2, y(1) = 1; use h = 0.1.
b. y" = ˆ’4xˆ’1y' + 2xˆ’2y ˆ’ 2xˆ’2 ln x, 1‰¤ x ‰¤ 2, y(1) = ˆ’1 / 2, y(2) = ln 2; use h = 0.05.
Example 2
The results are listed in Table 11.4. The first extrapolation is

the second extrapolation is

and the final extrapolation is

Table 11.4

4w(h 0.05) w(h 0.1) Extli 4w(h 0.025)w(0.05) Exti 16Ext2i Ext Ext,--15 wh 0.05) wdh = 0.025) 1.09262749 1.09262925 1.09262930 118707436 1.28337950 1.38144319 1.48115696 1.38144595 1.48115941 1.3814349:3 1.38144589 1.48115937 1.38144595 1.48115942 1 .68501 396 1.78889853 1.89392740 1.89392951