Doubt in solving IFFT

I am trying to solve a problem similar to the example provided in https://in.mathworks.com/help/symbolic/compute-fourier-and-inverse-fourier-transforms.html. I have doubt how to incorporate space and time function together using IFFT. Even I solved analytically, but results are different using complex analysis. My differential equation is of form:

EI*(d^4y/dx^4)+ky+m*(d^2y/dt^2)=Pδ(x-vt), −∞<x<∞ where delta is Dirac-delta function, v is velocity and t is time