  We describe how a dlog representation of Feynman integrals leads to simple
differential equations. We derive these differential equations directly in loop
momentum or embedding space making use of a localization trick and generalized
unitarity. For the examples we study, the alphabet of the differential equation
is related to special points in kinematic space, described by certain cut
equations which encode the geometry of the Feynman integral. At one loop, we
reproduce the motivic formulae described by Goncharov \cite{Goncharov:1996tate}
that reappeared in the context of Feynman parameter integrals in
\cite{Spradlin:2011wp,Arkani-Hamed:2017ahv}. The dlog representation allows us
to generalize the differential equations to higher loops and motivates the
study of certain mixed-dimension integrals.
