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We consider the equations $${u_{yy}} = {u_y}{u_{xx}} - ({u_x} + u){u_{xy}} + {u_x}{u_{y,}}{u_{yy}} = ({u_x} + {u_y}){u_{xy}} - ({u_{xx}} + 2){u_y}$$that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in the infinite-dimensional coverings naturally associated to these equations.

Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties