Suppose Euler’s method, with increment dx, is used to

numerically solve the differential equation dy/dx=f(x,y)

with the initial condition that (x0, y0) lies on the solution

curve. Let (x1, y1), (x2, y2), and so on denote the points

generated by Euler’s method, and let y = y(x) denote the

exact solution to the initial value problem. Which of the

following must be true?

Note: more than one are possible

I. y(3) = y(x3)

II. y2 = y1 + f (x1, y1) dx

III. x3 = x0 + 3 dx

My work:

I believe it is II and III.

III seems correct because dx is the change in x so if you multiply it by 3 and add it to the original it should give you x3. and II just looks like the Euler's formula.

Anyone willing to confirm or correct.