A Two-Component Generalization of the Integrable rdDym Equation

We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer-Finley equation, and the deformed Boyer-Finley equation. Also we find a B"acklund transformation between our generalization and Bodganov’s two-component generalization of the universal hierarchy equation.