PDE equation

Question

df/dt + df/dx = sin(kx-wt)

Answer 1

A special solution can be fairly easily guessed.   It is

 

f =  (1/(w -k)) cos(kx -wt) + C.

 

To this we would have to add a general solution to the homogenous equation  df/dx + df/dt = 0

 

This general solution looks like   A exp( i(x - t)) + B exp(-i(x -t))  for constants A and B.

 

This question looks like it comes from physics   with k being a wavenumber and w being a frequency.

However, there seems to be a dimensional inconsistency as the PDE is written.