DIFFERENTIAL EQUATIONS

REAL LIFE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN VARIOUS FIELD Assignment: Applications of Differential Equations Q1. Population Growth Model A certain population grows at a rate proportional to its current population. a) Form the differential equation representing this situation. b) Solve the differential equation and obtain the population as a function of time. c) Explain how this model is useful in real-life population studies. Q2. Newton’s Law of Cooling The rate of change of temperature of a body is proportional to the difference between its temperature and the surrounding temperature. a) Form the differential equation based on Newton’s Law of Cooling. b) Solve the equation to find the temperature of the body at any time. c) Mention one practical application of this law in daily life. Q3. Electrical Circuit (RL Circuit) In an RL circuit, the rate of change of current is proportional to the applied voltage minus the product of resistance and current. a) Write the differential equation governing the circuit. b) Solve the differential equation to find the current as a function of time. c) State the importance of this model in electrical engineering.