Shaky start in the cold
 

I have just bought BMW 520i 2002 and on start up in the morning, the car shook vigorously that I had to switch it off. When I restarted the car, l left it for about 10 mins and then switched it off again. On the 3rd time restart, the car ran smoothly without any shaking. The mechanic suggested it could be coil or the spark plugs but this sounded like a guess work. Can anybody please advise even though l read on a thread that the problem could be the PCV