  Identifying integrable coupled nonlinear ordinary differential equations
(ODEs) of dissipative type and deducing their general solutions are some of the
challenging tasks in nonlinear dynamics. In this paper we undertake these
problems and unearth two classes of integrable coupled nonlinear ODEs of
arbitrary order. To achieve these goals we introduce suitable nonlocal
transformations in certain linear ODEs and generate the coupled nonlinear ODEs.
In particular, we show that the problem of solving these classes of coupled
nonlinear ODEs of any order, effectively reduces to solving a single first
order nonlinear ODE. We then describe a procedure to derive explicit general
solutions for the identified integrable coupled ODEs, when the above mentioned
first order nonlinear ODE reduces to a Bernoulli equation. The equations which
we generate and solve include the two coupled versions of modified Emden
equations (in second order), coupled versions of Chazy equations (in third
order) and their variants, higher dimensional coupled Ricatti and Abel chains
as well as a new integrable chain and higher order equations.
