A: order 1, degree 1 - matches III.
B: order 2, degree 1 - matches I.
C: order 3; the term ey′ makes degree not defined (not a polynomial in derivatives) - matches IV.
D: order 2, degree 3 (highest power of d2s/dt2) - matches II.
So A-III, B-I, C-IV, D-II.