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:

The solution of a first order, variables separable differential equation

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