I will expand this question a little bit:

So, can we use the formula of general solution for wave equation or we should prove/derive it?

Yes, you are allowed to use every appropriate (relevant) formula given in the class without rederiving it (unless specifically asked to derive it first). Definitely you need to ask yourself: "can I apply a formula for a general solution?", "Can I apply D'Alembert formula?"

There is a subtle difference between

*allowed* and

*can*: you

*can* use any appropriate formula but it may happen that you are

*explicitly* asked to use some specific approach in which case you

*are allowed* to use only some specific formulae.

P.S. This is my first post here, so I am not sure if I am asking an appropriate question

Yes, it is a completely appropriate question.