In the ODEs for O(t) and C(t), 0(t) represents the probability the DNA is in the open state at time t and C(t) the probability the DNA is in the closed state at time t. A. Using that 0(1) + C(t) = 1 , eliminate the C equation and find a single equation that 0(t) satisfies. B. Solve for the steady state of this equation, Oss and find CSS . C. Solve for O(t) in terms of Oss and O(0). D. Write down Euler’s method applied to the ODE for 0(t), i.e. On+1 = ? E. By iterating Euler’s method backwards until you reach 0 (0), solve for O” in terms of just the ODE parameters, At, and n. F. Assume 0(0) = 0, Take the limit that Δ1 → 0 and n → oo in the formula you just derived with t = n Δt fixed. Show that your formula for O” converges to the exact solution O(t) you found above in this limit. (Hint for the last parts, look at how we showed Euler’s method converged for y, Ay and the general proof of convergence for Euler’s method.)