# What is the difference between an implicit ordinary differential equation and a differential algebraic equation?

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?

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–  lhf May 24 '13 at 23:49
Thanks. I was reading "Solving Ordinary Differential Equations" by Hairer and their explanation wasn't very clear, however, the book you recommended cleared things up. –  Kimusubi May 25 '13 at 19:47