The ODE solver HBT(11)9 is expanded into a differential algebraic equation (DAE) solver, called HBT(11)9DAE, for nonstiff and moderately stiff systems of fully implicit DAEs. Pryce’s structural pre-analysis and automatic differentiation for DAEs is adapted to the new solver. The stepsize is controlled by a local error estimator. HBT(11)9DAE uses only the first five derivatives of y as opposed to 11 with the Taylor series method of order 11. HBT(11)9DAE is applied to electric circuit problems, and, on the basis of the CPU time and the maximum global error, it is superior to Dormand – Prince’s DP(8,7)13M adapted to solve DAEs.