Solve the following differential equations using the substitutions given. (a) (b)

A rectangular tank with its base horizontal is filled with water to a depth h at time t = 0. Water leaks out of the tank from a small hole in the base at a rate proportional to the square root of the depth of the water. If the depth of water is ½h at time T, find […]

A researcher is investigating the spread of a certain disease in a town with a population of 3000 people. The researcher suggests that I, the number of people infected by the disease at time t days satisfies the differential equation , where k is a positive constant. (i) Given that I = 30 when t = 0, […]