NOTE 19DD: The exact result can be found using the methods of Box 28.2. We have *du/dt* = (*dp/dt*)(1 – *u*_{0}) exp(–*ct*). Now, we know that *p*_{t}/*q*_{t} = (1/2*N*) exp(*st*), and so exp(–*ct*) = (2*N* *p*_{t}/*q*_{t})^{–c/s}, and

Treating *u* as a function of *p* (as in Box 28.2), we have

This does not have an explicit solution, but for 2*N* large is very close to (2*N*)^{–c/s}, as given by the simple argument above.