How can I use one database connection object in whole application?

I have created this class which returns connection object. I have used MySQL database.

public class Connect_db {        
    public Connection getConnection(String db_name,String user_name,String password)
    {
        Connection con=null;
        try
        {
        Class.forName("com.mysql.jdbc.Driver");
        con=DriverManager.getConnection("jdbc:mysql://localhost/"+db_name+"?user="+user_name+"&password="+password);
        }
        catch(Exception e)
        {
            e.printStackTrace();
        }

        return con;        
    }
}  

Now all I want to do is instantiate this class once and get connection object. And I want to use this same object in entire application. Another solution will also be appreciated.