We should only deal with what is actually posted.
If we begin to guess as to what the question might mean, then we do a real disservice.
Because, the question may well mean actually what it says, which I suspect is the case here.
My friend helped me solve it .. the question was written very confusing.. and actually asked for something completely different . I appreciate all the suggestions and help though!
I totally agree with my colleagues, it does not make sense, function with independent variable x and derivative wrt t. The question is definitely wrong. Either the derivative should be wrt t or the independent variable should be x.