  Differential equations are powerful tools in the study of correlation
functions in conformal field theories (CFTs). Carrollian amplitudes behave as
correlation functions of Carrollian CFT that holographically describes
asymptotically flat spacetime. We derive linear differential equations
satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain
non-distributional solutions for both the gluon and graviton cases. We perform
various consistency checks for these differential equations, including
compatibility with conformal Carrollian symmetries.
