Delayed Differential Equations with multiplicative terms

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I am not a DDE expert so before solving this equation with numerical methods, I wanted to ask from experts if a closed form solution exists. After some change of variables I could simplify my delayed differential equation as $ f'(x) = xf(x) + af(x+\tau)$. Is there an analytic solution for such classes of DDEs or I should solve it numerically after all?