Final answer:
The explicit solution is found by integrating both sides of the differential equation and using the initial condition y(9) = 9 to determine the constants.
Step-by-step explanation:
The explicit solution for the initial-value problem dy/dx = (y² - 1)/(x² - 1), with the initial condition y(9) = 9, is sought using the method of separation of variables or potentially another applicable differential equations technique. We recognize that the y-intercept does not exist since the equation is not defined for x = 1. Hence, the solution involves integrating both sides and then applying the initial condition to find the specific solution satisfying y(9) = 9.