# Math Help - Eulers Method Multiple Choice

1. ## Eulers Method Multiple Choice

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.

2. Yes, you are right. Both II and III are true. I is just meaningless- there is no reason to think that "x3" is actually the number "3".