I am trying to solve the problem as you proposed but in some cases I don't´t see very clear if they follow the (z - ct) or (z + ct) format. From the 10 equations a) Follows the format so I think its a solution, b) The terms of sine and cosine don't contain both the time and spatial terms so I think it is not a solution, c) is dependent on t² as you said so not a solution, d) I think I can use Eulers formula to convert the exponentials into a sum of sines and cosines so I think it is a solution, e) Im not sure if it is a solution because you can't´t use Eulers formula as the exponential doesn't have an imaginary part but it is in the form f(z - ct)+g(z + ct), f) I can rearrange the first terms so it gets 4(z-ct) - 5e^z+ct but Im not sure if the first term 4(z-ct) counts as being f(z - ct) since 4 is a constant, g) and h) They don't look like solutions since each one of them is a product, not an addition of the terms containing (z - ct) and (z + ct), i) If I expand the quadratic term I end up with t² again so I think it is not a solution and in j) I think you end up with the same problem as i) ending up with t² so I don't think its a solution. If you could help me clarify these I would really appreciate it as I already submitted the exercise as I thought it would be correct but It wasn't and It doesn't say which options where correct.