Reductions of the universal hierarchy and rdDym equations and their symmetry properties

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