I'm rather confused on this particular point. What is the difference between an implicit ordinary differential equation of the form:
x' = f(x',x,t);
and a differential algebraic equation of the form:
f(x',x,t) = 0;
I've read some documentation on them online, and while some places mention that implicit ODEs are a special class of DAEs, they're not very clear on the point. Also, is there any specific consideration that needs to be made in regards to numerical solutions of such problems?