Hint

There will be 4 steps, involving lines at x = 0, x = 0.25, x = 0.5, and x = 0.75

Answer

First Step: We start at the point (0,0) and draw a line to estimate y(.25). The slope of this line is

We have

Second Step: We start at the point (.25,0) so that y_old = 0 and draw a line to estimate y(.5). The slope of this line is

Then we can estimate

Third Step: We start at the point (0.5, 0.125) so that y_old = 0.125 and draw a line to estimate y(0.75). The slope of this line is

Then we estimate

Fourth Step: We start at the point (0.75,0.375) so that y_old = 0.375 and draw a line to estimate y(1). The slope of this line is

Then

Our final estimate, using Euler's method, is that

y(1) ≅ 0.75.