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I'm interested in finding the (unique?) solution to the set of delay differential equations $$f_w(w,x) = xf(w,w^2x)+w^3x^2f(w,w^4x), $$ $$f_x(w,x) = wf(w,w^2x)$$ With the initial condition $f(1,x) = e^...

Assume a function $f(x)$ is given numerically for $x>0$, i.e. for any $x>0$ there is a numerical procedure to obtain $f(x)$ to any desired precision. Also assume that the function $f(x)$ has a ...