Open Question: differential equation; separation of variables dx(t)/dt = k(a-x(t))(b-x(t))?
16:02 Publicado por Flechado16
Start: dx/[(a-x)(b-x)] = kdt
1/(a-x)(b-x) = [A/(a-x)] +B/(b-x) => A = 1/(b-a) B=1/(a-b)
The integrand is then [1/(b-a)][1/(a-x) - 1/(b-x)], which integrates to [1/(b-a)]ln{(b-x)/(a-x)} and kdt just integrates to kt.
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