Below is a workaround for the simple case. The OP can say whether it works more general. I haven't quite tracked down yet why the system is set up incorrectly with the default `Method -> {"EquationSimplification" -> "Solve"}` and with `Method -> {"EquationSimplification" -> "Residual"}`. But it works in this case with `Method -> {"EquationSimplification" -> "MassMatrix"}`. simDAE = First@ NDSolve[{x[0] == 100., x'[t] == 0.05 x[t] + deposit[t], y[0] == 1., y[t] == 1. }, {x, y}, {t, 0, 10}, Method -> {"EquationSimplification" -> "MassMatrix"}]; Plot[Evaluate@(x[t] /. simDAE), {t, 0, 10}] ![Mathematica graphics](https://i.stack.imgur.com/I8Elp.png)