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http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

it is said that if

ds/dt = -b*s(t)*i(t) is divided by dr/dt= ki(t) and is integrated by using chain rule, the answer is S(t) = S(0)exp (-Ro(Rinf - R(0))

but if i solve it, answer i get is r = 1/Ro * lns + c

i have no clue how can i get this answer.

Can anyone help me understand this please.