Exactly what are you supposed to do to open the chest located on the roof of Philippa Eilharts room ?

Did you grab Phillipa's notes from her desk? There should be a couple diagrams on there. Those diagrams show numbers in different spots. Not sure if there's a faster way, but I ran through all three of them going from lowest number to highest number, first diagram first, second second, etcetera. That worked for me, so hopefully it works for you.

Yea, i found the diagram but i dont understand exactly what to do with. Are you suppose to light the candles in some order or something ?

Yep. The candles line up with the position of the numbers in the diagram, so you light the candles in order.

Stand facing the chest and light candles in order shown on the diagram. I first, II second etc.

Do you use Igni for this ?

No, you should be able to face the candle and left-click to light. There should be a prompt.

There must be a bug in my game then because im not getting a prompt. I'll try saving and reloading, ill post back if i got it to work.

I see, that must be what it is then. When i found the chest i was by myself.

Yeah, then you won't be able to do anything there. If the story brings you there, you'll be able to open it. Otherwise don't worry about it :)

EDIT: Mark as solved, please. Otherwise people will keep coming in and saying the same thing.

So you got to philpha's room without the quest? I had assumed it would be locked..

Which path are you on and how did you get to her room (sewers?).