We are required , at Leaving
Certificate higher level, to be able to solve differential equations of
two types:

1. First order, variables
separable

2. Second order, reducing
to type 1.

A differential equation
is one which contains a derivative.

Type1 example : | |

Type 2 example: |

Method of solution:

Step 1: Separate the variables

Step 2: Integrate

Step 3: Substitute the
initial conditions

**An example of the solution
of a first order variables separable differential equation**

*Leaving Certificate 1999.
Higher Level question 10 (a)*

Solve the differential equation

given that v = 0 when x
=1.

**Suggested solution**

Step 1. : Separate the
variables

**Note:** the initial
conditions v = 0 when x = 1 have become the lower limits for the integration.

Step 2: Integrate

Step 3: Substitute