Especially in physics there are some types of equations that in their subfield are called master equations. Examples include the following:
in BV-BRST formalism the classical master equation is the condition that the refinement of an action functional to a function on its derived critical locus squares to 0 with respect to a certain graded Poisson-bracket. The quantum master equation is a deformation of this equation. See at BV-BRST formalism for details on all this.
in statistical mechanics, Langevin equation and generalizations
linear evolutionary differential equations (often for operator functions) of the form $d y/ d t = L y$ where $L$ is a linear operator not involving differentiating with respect to time is sometimes called a master equation in some contexts
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