Is there literature available on solving differential equations of the type $f(x,y(x),y(\kappa x),y'(x))=0,$ where $\kappa$ is a given constant? I know about the book Introduction to the Theory and Application of Differential Equations with Deviating Arguments by L.E. El'sgol'ts and S.B. Norkin from the year 1973 [1], but I wonder if there are more recently published books available as well.
Specifically, I would be interested in solving for example $u(2t)-2u'(t)u(t)=0$ without guesswork.
[1] Introduction to the Theory and Application of Differential Equations with Deviating Arguments, L.E. El'sgol'ts and S.B. Norkin, Mathematics in Science and Engineering, Volume 105, Academic Press, New York, 1973