I have the following differential equation:
It is suppose to be non integrable for a differentiable but arbitrary $f(t)$. How do I know this is true?
This is part of the problem 1.6 in Goldstein's Classical Mechanics 3rd edition book. Also, in the text it says that, in principle, an integrating factor always can be found for any first order differential equation that involves only two variables. How can I prove this statement?