[Hitchhiker 42]

Originally Posted by Ether

Yes, but you got x and t confused.

given:

x(t) = 1/4*t^3 + 1

... take time derivative of x(t) to get:

x'(t) = (3/4)*t^2

...take time derivative of x'(t) to get:

x''(t) = (3/2)*t


Now solve for the differential equation:

solve x'(t) for t:

x'(t) = (3/4)*t^2 => t=sqrt(4x'(t)/3)

... and then substitute for t in x''(t):

x''(t) = (3/2)*t = (3/2)*sqrt(4x'(t)/3) = sqrt(3*x'(t))

I see... so that column is in terms of x', not t. I've updated the spreadsheet to reflect that and it seems to show that the Euler method does better.
dt = 0.01s, error measured at t=3s.

Euler error: 0.2061
Midpoint error: 5.0828

This, I presume, is for the reason I mentioned in my first post.