Mathematics Pure Math 2,3 9709: DIFFERENTIAL EQUATION Topical Past Paper Questions

A curve is such that the gradient of the curve at any point is proportional to the y-coordinate at that point. The curve passes through the points $(2, \mathrm{e}^{2})$ and $(5, \mathrm{e}^{3})$. Form and solve a differential equation to find $y$ in terms of $x$. [7]

A fungal disease is affecting some of the trees in a forest. The fraction of the trees affected after t years is denoted by x. The rate of increase of x is proportional to the product of the fraction of the trees affected and the fraction of the trees not affected. (a) Explain wh…

A water tank is in the shape of a cuboid with base area $ 40\,000\,\text{cm}^2 $. At time $ t $ minutes the depth of water in the tank is $ h $ cm. Water is pumped into the tank at a rate of $ 50\,000\,\text{cm}^3 $ per minute. Water is leaking out of the tank through a hole in t…