A chemical dissolves in water at a rate jointly proportional to the amount undissolved and to the difference between the concentration in the solution and that in the saturated solution. Initially none of the chemical is dissolved in the water. Show that the amount x(t) of undissolved chemical satisfies the differential equation

where k is a constant, M is the amount of the chemical in the saturated solution and x₀ = x(0).

Transcribed Image Text:

dx dt = kx(M - xo + x)