Final answer:
The given equation represents a non-homogeneous wave problem in physics that can be solved by separating the homogeneous and non-homogeneous parts and solving them separately.
Step-by-step explanation:
The given equation represents a non-homogeneous wave problem in physics.
In this equation, u represents the displacement of the wave in the x-direction, t represents time, and f represents the external force acting on the system. The equation also includes derivatives with respect to time (ut and utt) and the second derivative with respect to x (uxx).
To solve this type of problem, one approach is to separate the homogeneous and non-homogeneous parts of the equation and solve them separately. The homogeneous solution will represent the natural oscillations of the system, while the non-homogeneous solution will capture the effect of the external force.