The Failure in Computable Analysis of a Classical Existence Theorem for Differential Equations
Oliver Aberth · Proceedings of the American Mathematical Society · 1971
An example is given of a uniformly continuous constructive function $f(x,y)$ with $f(0,0) = 0$, such that the differential equation $y’ = f(x,y)$ with the initial condition $y(0) = 0$ has no constructive solution.