Chapter 2.2, Problem 25P

Use the alternatives forms $\begin{array}{l}x\left(t\right)=\frac{N\left(x_0-H\right)+H\left(N-x_0\right)e^{-k\left(N-H\right)t}}{\left(x_0-H\right)+\left(N-x_0\right)e^{-k\left(N-H\right)t}}\\ =\frac{H\left(N-x_0\right)e^{-k\left(N-H\right)t}-N\left(H-x_0\right)}{\left(N-x_0\right)e^{-k\left(N-H\right)t}-N\left(H-x_0\right)}\end{array}$ of the solution in (15) to establish the conclusions stated in (17) and (18).