The Hodgkin-Huxley model for excitable nerve cells is a set of four differential equations, three of the form

where y is a variable between 0 and 1 related to potassium channel activation, sodium channel activation, or sodium channel inactivation in the cells, and a and b are rate constants.

(a) Solve this equation with the initial condition y(0) = y₀.
(b) What is the limit of the solution from part (a) as t goes to infinity?

dy = a(1 - y) - By, dt