The differential equations are modeled from real-life scenarios.
- Newton’s second law is described by the differential equation
m d2h / dh2 = f(t,h(t), dh / dt)- where m is the mass of the object, h is the height above the ground level. This is the second-order differential equation of the unknown height as a function of time.
- As time increases, the population increases. If r > 0 is the growth rate, then the differential equation modeling the population is given as dN/dt = rN.
- The rate at which the disease spreads is proportional to the product of the infected people with the non-infected people. This is modeled as dN/ DT = k N(T-N), where T is the fixed population and N is the number of people affected by the disease.
- For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature. dP/dt = k P/T^2