  In two-dimensional CFTs with a large central charge, the level-two BPZ
equation governs the heavy-light scalar four-point correlator when the light
probe scalar has dimension $h= - {1\over 2}$; the corresponding linear ordinary
differential equation can be recast into a schematic form $x^2 u_{xx}+u=0$. In
this paper, we make an observation that in a class of four-dimensional CFTs
with a large central charge, the heavy-light scalar correlator in the
near-lightcone limit obeys a similar equation, $x^3 u_{xxxy}+u=0$, when the
light scalar has dimension $\Delta=-1$. We focus on the multi-stress tensor
sector of the theory and also discuss the corresponding equations for the cases
with $\Delta = -2, -3$. The solutions to these linear partial differential
equations in higher dimensions are shown, after a suitable change of variables,
to reproduce the near-lightcone correlators previously obtained via holography
and the conformal bootstrap.
