The O(h^2) term on line (3) should be subtracted from the right hand side not added, because the terms with third degree derivatives are brought to the other side so their signs must change.
I understand your point, but the sign in this case does not matter.
The O(h^a) terms are generic notation
for a constant (independent of h) times h^a, plus higher order terms,
so it does not matter whether you say O(h^a) or -O(h^a).
And when I say it is of the form …, I mean generic form.
But feel free to change the form with a minus before h^2 / 3.
Got it, thank you!