DependentVariables is an option to NDSolve which specifies the list of all objects that should be considered as dependent variables in the equations supplied.
NDSolve[eqns, {y1, y2, ...}, ...] specifies that NDSolve should return solutions for the yi.
DependentVariables->{u1, u2, ...} specifies a complete list of dependent variables ui representing functions that should be solved for, even if the solutions are not eventually returned.
EXAMPLES
Basic Examples 
Applications