What follows is an example on how to solve a BVP using the Laplace Transform. I will copy and paste the example and its solution from the book that I am using and then I will ask my question.
When finding $U(x,s)$ you first find the general solution to the associated homogeneous equation $\frac{d^2U}{dx^2}-s^2U=0$. To me it seems like the book is assuming that $s\neq0$, since $U_c(x,0)=c_1+xc_2$. I was wondering if you see a reason why $s$ cannot be $0$.