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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

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