The Nobel Prize in Physiology or Medicine in 1963 was shared by A.L. Hodgkin and A. F. Huxley in recognition of their model for the firing of neuronal synapses. They proposed that the opening/closing of certain ion channels in the neuron cell was governed by a combination of probabilistic "gating variables", each satisfying a differential equation that they expressed as

du/dt = α(1 - u) - βu with positive parameters α and β

Solve the equation and show that all solutions approach the value α / α + β exponentially