  The differential transform method is used to find numerical approximation of
solution to a class of certain nonlinear differential algebraic equations. The
method is based on Taylor's theorem. Coefficients of the Taylor series are
determined by constructing a recurrence relation. To deal with nonlinearity of
the problems, the Fa\`{a} di Bruno's formula containing the partial ordinary
Bell polynomials is applied within the differential transform to avoid
computation of symbolic derivatives. The error estimation results are presented
too. Four concrete problems are studied to show efficiency and reliability of
the method. The obtained results are compared to other methods.
