Often Ordinary Differential Equations (ODE’s) are studied in engineering, especially system dynamics and control theory. However, there are many cases where the system is described by Differential Algebraic Equations (DAE’s) rather than an ODE system.

Here are some resources related to the issue:

Computer methods for ordinary differential equations and differential-algebraic equations is the most famous book on DAE’s I have come across. When you read articles on DAE’s, the author usually references the following book.

Ascher, Uri M., and Linda R. Petzold. Computer methods for ordinary differential equations and differential-algebraic equations. Vol. 61. Siam, 1998. https://goo.gl/vmpq5l

I came across this book related to control theory and DAE’s

Berger, Thomas. On differential-algebraic control systems. Diss. Technische Universität Berlin, 2013. http://goo.gl/w4m5ms