The general differential equation I am interested in is the following
$$ \left[a\frac{\partial^4}{\partial x^4} + b\frac{\partial^2}{\partial t^2} + c\frac{\partial}{\partial t} + d\frac{\partial^4}{\partial x^4}\frac{\partial}{\partial t}\right]v(x,t) = f(x,t)$$
where f(x,t) is a generic source term. Therefore, I am trying to compute the Green's function associated to the operator in brackets.
It's been a while, and I'd like to have your expert opinion of the best way to approach this. Do you think going to Fourrier space could yield a closed solution, or is there anything smarter to apply here ?
Any feedback appreciated