Week 1 and 2.
The input of this procedure is the following: f is a function in x, and M in C(x)[Dx] is an operator for which M(f)=0. The output of the procedure IntSol should be either FAIL (if there exists no L in C(x)[Dx] for which D:V(L)-->V(M) is 1-1 and onto) or an antiderivative r(f) of f otherwise. Give an example where the procedure returns FAIL and another example where it returns an antiderivative of f. Use your procedure to integrate f:=erf(x) (you first have to find an operator M in C(x)[Dx] for which M(f)=0. This operator turns out to have order 2. Find M by computing f, diff(f,x), diff(f,x,x) and then searching for rational functions a0,a1,a2 for which a0*f+a1*diff(f,x)+a2*diff(f,x,x)=0).