Applications of First Order Differential Equations

Tutoring on Applications of First Order Differential Equations

Learning Objectives:

Understand and apply First Order Differential Equations

Math Tutoring on Applications of First Order Differential Equations

Some of the important Applications of First Order Differential Equations are – 

1.   Exponential Growth or Uninhibited Growth & Exponential Decay:

This models Exponential Growth which means the rate of growth is proportional to the population or amount. This can also be used to model Continuous Interest.

We will solve this differential equation to find P(t), but the only function that satisfies this is

If, the above model explains Exponential decay, which means the rate of decline or decay is proportional to the population or amount.

 

2.   Problems regarding Mixtures of Two Solutions:

A(t) is the amount of the substance dissolved in the liquid in the tank at any time t.

Liquid is entering and leaving a tank. The liquid entering the tank will contain a different concentration of substance dissolved in it.

 

3.   Newton’s Law of Cooling:

The temperature T of a cooling object drops at a rate that is proportional to the difference T - C, where C is the surrounding Constant Temperature.

We will solve this differential equation to find T(t), but the only function that satisfies this is

 

 

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Hook Question:

1.   Give some example of Applications of First Order Differential Equations.

 

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