In Maths T, you learnt how to solve 2 types of differential equations, namely the **separable variable **and the **homogeneous **differential equations. In FMT, you will learn how to solve **linear differential equations**.

A differential equation is linear if it is of the form

where **a** is a function of x. It can be solved by introducing an **Integrating Factor**, **e ^{∫ a dx}**. This term is multiplied to the left and right of the equation, then we will get

integrating both sides, we get

Which is an expression of y in terms of x. This method is very simple, let me give you an example:

*Find the general solution of the differential equation*

We start by expressing it in the form

Now that we know the **a**, we can find the integrating factor,

Note that the integration in the integrating factor doesn’t need a constant, because it will eventually cancel out later. So multiplying it both sides,

Probably one of the easiest sections, so don’t make mistakes. Notice that the x is not handed over **before **the integration is done. A common mistake is that you tend to forget to multiply the integrating factor to the **right hand side**. So be extra careful in calculations. This is the general solution, and the **particular solution** can be found if more details are given (for example when **y = 1**, **x = 1**). Practise. ☺

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