## Elementary Differential Equations – Rainville

I finished the first two chapters of Elementary Differential Equations by Rainville. This is the second edition circa 1958, and there is an 8th edition now. This was a very through start into ODEs. I wouldn’t have understood most of it without the MIT lectures. This is my Dad’s book! A couple of specific notes:

Chapter 1 – it is possible to move from a solution with arbitrary constants back to the differential equation, by differentiating and solving for each of the constants and substituting back in. differentiations for constants.

Chapter 2 – **homogeneous functions** have all terms to the same degree. The substitution could be or whatever is simpler. Pg. 29 discusses **exact equations** where are of the form

where . If an equation is not exact it might be made so by an **integrating factor**.

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