Thread: Tricky Implicit Differentiation

Hi,

How could I possibly differentiate x = a - 1/(kt-c) where c is an integration factor in order to provide the equation

dx/dt = k(a-x)(b-x)

assuming that a = b

$\displaystyle \frac{dx}{dt}=\frac{k}{(kt-c)^2}=k\left(\frac{1}{kt-c}\right)\left(\frac{1}{kt-c}\right)=k\left(a - a - \frac{-1}{kt-c}\right)\left(a - a - \frac{-1}{kt-c}\right)=k(a-x)(a-x)$