arXiv:2608.01472v2 Announce Type: replace Abstract: We consider the boundary value problem $y''=\kappa^2y^n, y(0)=1, y(1)=0,$ relevant to radiative heat transfer, chemical reactions, etc. We use upper/lower envelopes to study the qualitative and quantitative dependence of its solution on parameters, and transform it into an easily solvable initial value problem.