Write out the differential equations, DO NOT solve, for the following word problems. a. The acceleration, v'(t), of a coasting motorboat is proportional to the square of its velocity, v(t).
b. The population of Zootopia in year t, is P(t): Animals are born at a rate propor­tional to the population. The death rate is also proportional to the population. Animals move to Zootopia at a rate of 50,000 animals a year, and 40,000 animals move away in a year.
c. A function g(x) is described by the following property of its graph: At each point (x, y) on the graph y=g(x), the normal line to the graph passes through the point (0, -2). Use this information to find a differential equation of the form: dy/dx = f(x, y) Having the function g(x) as its solution.