First-Order Differential Equations (College Board AP® Calculus AB)

A portion of the slope field for the differential equation is given below.

Sketch the solution curve through the point .

A cylindrical tank contains water and is being used to fill up a garden pond. The tank is standing upright on its circular base. The rate of change of the height of the water in the tank with respect to time is modeled by , where is measured in feet and is measured in seconds.

At time seconds, the height of water in the tank is 4 feet. Use separation of variables to find an expression for in terms of .

Scientists are studying a population of leopards in a nature reserve. The rate of change of the population is proportional to the difference between the current population and the maximum population that the reserve can support. If is the population at time months after the start of the study, then

Use separation of variables to find the particular solution to the differential equation with initial condition . Give your answer as an expression for in terms of .

Use separation of variables to find , the particular solution to the differential equation with the initial condition .