Write down a differential equation of the form dy/dt=ay+b whose solutions all approach y = 6 as t?? Solution dy/dt = a*y + b = a*(y + b/a) is a separable equation: dy/(y + b/a) = a dt Integrating: ln(y + b/a) - ln(c) = a*t where ln(c) is the constant of integration. ln((y + b/a)/c) = a*t y(t) = c*exp(a*t) - b/a Now, for this solution to be bounded as t -> infinity, a must be < 0. When a < 0, the exponential term goes to zero as t-> infinity, so: y(t -> infinity) = -b/a for a < 0 We therefore want -b/a = 6 There are an infinite number of possible solutions that meet the criteria in this question.