Ignoring all forces except the Earth’s gravity find the speed with which you must launch a rocket so that it never returns to Earth.
The population of a town at time is 365. The population growth factor is , and the town experiences a death rate of one percent of the population per day. Find a differential equation modeling the population of the town as a function of time and find
- the actual population of the town after years,
- the cumulative total of the fatalities from the town’s death rate.
A given substance decays at a rate proportional to the squareroot of the amount of the material present. Show that a substance with this decay property will completely decay in a finite amount of time and find this time.
A given substance decays at a rate proportional to the square of the amount of the material present. At the end of one year there is 0.5 grams of the substance remaining.
- Create and solve a differential equation that governs the mass of the material present after years.
- Find the decay constant of the material in units .
Consider the differential equation
Make a change of variable where is a function of and is a constant and solve the differential equation.
Use a change of variables to convert the following differential equation into a linear differential equation, and then solve the equation:
Assume the differential equation
has a solution of the form
for some constant . Determine an explicit formula for this solution.