  We study a class of unbalanced constant-differentials P\'olya processes on
white and blue balls. We show that the number of white balls, the number of
blue balls, and the total number of balls, when appropriately scaled, all
converge in distribution to a gamma random variables with parameters depending
on the differential index and the amount of ball addition at the epochs, but
not on the initial conditions. The result is obtained by an analytic approach
utilizing partial differential equations.
