Numerical Solution of Differential-Algebraic Equations

The example:

    (1) x''(t) + y(t) = cos(t)
    (2) x(t) = cos(t)

is trivially solvable by differentiating (2) twice and substituting into (1) to give:

    -cos(t) + y(t) = cos(t)

or

    y(t) = 2 cos(t)

Together with (2) that gives the solution; there is no need to use advanced techniques to solve this particular example.