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There are 3 subtopics in this chapter:
i) Separable Variables
ii) First Order Linear Differential Equations
iii) Applications
In this chapter, you will be given a first order differential equation and you will need to solve it. Basically, you only need to choose between separate the variable or by using integrating factors. As long as you cannot separate the variable, it will be the case of using integrating factor. Choose wisely! Sometimes you might need to factorise or expand the function first before you can separate the function.
Then, you will attempt to solve problems involving first order differential equations. You are not expected to formulate the differential equations. But, you are expected to solve any applications problems including Newton's Law of Cooling, electric circuit, population growth and radioactive decay.
This method is use when we can separate the variables (one variable on the left, another variable on the right).
P/s:
You can have either general or particular solution. If you are given some boundary conditions, then you can have a particular solution. Otherwise, you will have a general solution.
Can you find the murderer, victim and suspects?
This method is use when we can not separate the variables. Hence, you need to make sure to write them in the general form and follow the given steps.
P/s:
Again, check if the questions give you a boundary conditions or not.
There are many applications of first order differential equations. Some examples are Newton's Law of Cooling, Electric Circuits, Population Growth and Radioactive Decay.
Separable Variable + Linear Differential Equations + Applications