  We propose here a new model termed as the Differential Equation Model for the
ground to first 2+ state excitation energy E2 of a given even-even nucleus,
according to which the energy E2 is expressed in terms of its derivatives with
respect to the neutron and proton numbers. This is based on a similar
derivative equation satisfied by its complementary physical quantity namely the
Reduced Electric Quadrupole Transition Probability B(E2) in a recently
developed model. Although the proposed differential equation for E2 has been
perceived on the basis of its close similarity to B(E2), its theoretical
foundation otherwise has been clearly demonstrated. We further exploit the very
definitions of the derivatives occurring in the differential equation in the
model to obtain two different recursion relations for E2, connecting in each
case three neighboring even-even nuclei from lower to higher mass numbers and
vice-verse. We demonstrate their numerical validity using the available data
throughout the nuclear chart and also explore their possible utility in
predicting the unknown E2 values.
