Reference Request: introductory text for advanced type of differential equation

Question

I am looking for an introductory reference to advanced differential equation, for example $x'(t) = x(t+1)$. The term "advanced" makes the search quite challenging using Google. The topic is sometimes introduced in-passing in other delay or functional textbook. Perhaps something at the level of "A First Course in Integral Equations" by Abdul-Majid Wazwaz is most appropriate. Thanks!