Question on Euler's method - ODE

[cue928]

Homework Statement

y' = y - x - 1, y(0) = 1, h = .25

Homework Equations

The Attempt at a Solution

y1 = 1+(.25)*(1-0-1) = 1
y2 = 1+(.25)*(1-1-1) = .75

This is not what the book has, but it is organized weird to me. It asks for EM twice, first w/ step size h=.25, then h=0.1. But the way the answers are listed in the back do not correspond with this so I am not sure what they are getting. Curious if folks agree w/ me here on y1, y2. Thanks in advance.

 

[gabbagabbahey]

Homework Statement

y' = y - x - 1, y(0) = 1, h = .25

Homework Equations

The Attempt at a Solution

y1 = 1+(.25)*(1-0-1) = 1
y2 = 1+(.25)*(1-1-1) = .75

This is not what the book has, but it is organized weird to me. It asks for EM twice, first w/ step size h=.25, then h=0.1. But the way the answers are listed in the back do not correspond with this so I am not sure what they are getting. Curious if folks agree w/ me here on y1, y2. Thanks in advance.

Why are using using $x_2=1$?