Differential equations — practice question

A broad field with area $4\,\text{km}^2$ is being affected by a soil disease. At time $t$ years, the diseased area is $x\,\text{km}^2$, and its growth rate is described by the differential equation $\frac{dx}{dt} = kx(4 - x)$, where $k$ is a positive constant. It is given that when $t = 0$, $x = 0.4$ and that when $t = 2$, $x = 2$.