1. Chapter 5
APPLICATIONS OF ODE

2. OVERVIEW LAW of GROWTH or DECAY LAW of COOLING CHEMICAL REACTIONS
ELECTRIC CIRCUITS

3. Rate of change of a quantity proportional to the quantity present
Law of Growth or Decay
Rate of change of a quantity proportional to the quantity present

4. Law of Growth or Decay
The number of bacteria in a culture grows at a rate proportional to the number of bacteria present. The number triples in 1 hour. If the initial number is 10, find:
The number of bacteria after 5 hours.
2) After how long the number was exactly 270.
1) 2430
2) 3

5. Law of Cooling Temperature of the hot substance
Temperature of the surrounding

6. Law of Cooling
A cup of Coffee at 90⁰C is placed in a room at 25⁰C. In 5 minutes, it cools to 70⁰C. Find
1) The temperature of the cup after another 5 minutes.
2) After how long the cup will be exactly at 27⁰C.
1) 56.15
2) 47.33

7. Chemical reactions - Solutions
Amount of salt in the tank
Volume tank
Concentration of incoming mixture
rate of incoming mixture
rate of outgoing mixture

8. Chemical reactions - Solutions
A tank contains 100 liters of brine (solution of salt) in which 500g of salt is dissolved. If brine containing 20 g of salt per liter runs into the tank at the rate of 3 liters per minute and the mixture, which is kept uniform, runs out of the tank at the rate of 2 liters per minute, find the amount of salt in the tank after exactly 30 minutes.

9. Electric circuits
L-R-C circuit, where R (resistance), L (inductance), and C (capacitance) are in series, and acted on by an electromotive force E.
The current satisfies:
The current is the rate of flow of the positive charge : 

10. Electric circuits
A voltage is applied at at a circuit containing an inductance L and a resistance R. Assuming , show that the current in the circuit is: