Question

convert the system shown into a system of first-order equations:
(x'')^2 +te^y + y' = x'-x
y'y'' - cos(xy) + sin(tx'y) = x

question: my book introduces the following variables:: x_1 = x, x_2 = x', x_3 = y, and x_4 = y'

can someone clarify why they chose it this way and not: x_1 = y, x_2 = y', x_3 = y'' and x_4 = y''' like they did in a previous example