  A method has been developed for obtaining equivalent linear two-body
equations (ELTBE) for the system of many ($N$) bosons using the variational
principle. The method has been applied to the one-dimensional N-body problem
with pair-wise contact interactions (McGurie-Yang N-body problem) and to the
dilute Bose-Einstein condensation (BEC) of atoms in anisotropic harmonic traps
at zero temperature. For both cases, it is shown that the method gives
excellent results for large N.
