Use Eulers Method interval is 0 12 with step size 25 y y x

Use Euler\'s Method. interval is {0, 1/2} with step size .25

y\' = y - x - 1, y(0) = 1; y(x) = 2 + x - e^x

Solution

y(0) = 1 ; h = 0.25

y\'(x) = y - x - 1

y\'(0) = y(0) - 0 - 1 = 1-1 = 0

y(0.25) = y(0) + hy\'(0)

=> y(0.25) = 1 + 0.25*0 = 1

y\'(0.25) = y(0.25) - 0.25 - 1 = -0.25

y(0.5) = y(0.25) + h*y\'(0.25)

=> y(0.5) = 1 + 0.25*-0.25

=> y(0.5) = 0.9375