Newtonian energy integral and suitable boundary conditions

[Matter_Matters]

I have a (somewhat) strange energy equation which has the following form:
[tex] KE = A + B W + C \exp(-D W), [/tex]
where [itex] A,B,D [/itex] are known constant, [itex] C [/itex] is an unknown constant to be determined and kinetic and potential energy are given by [itex] KE [/itex] and [itex] W [/itex] respectively with [itex]W\equiv W(r)[/itex] i.e. is a function of position only and [itex] KE \equiv KE(t) [/itex] i.e. is a function of time only.
Question:
What conditions could I use (boundary or initial) that would suggest [itex] C = 0 [/itex]?
I have tried something like
[tex]
\lim_{r \rightarrow \infty} W(r) = 0, \\
KE(t=0) =0.
[/tex]

 

[LightHero]

But, I am not sure if these are sufficient or if there is something else that I need to consider?Any help would be appreciated.