For the differential equation
$$\frac{d}{dx}[y(x)]=y^{(-1)}(x)$$
where $y^{(-1)}(x)$ is the inverse of $y(x)$, find y(x).
I gave up on finding the solution analytically pretty quickly and decided that a numerical approach might be more effective. But, I'm not sure that this problem can be solved, even numerically; an Euler or Runge-Kutta type method will not work because to find the value of $y^{(-1)}(a)$, one must first know the value of $y(b)$, where $a$ is not necessarily equal to $b$. Sort of like trying to solve $\frac{d}{dx}[y(x)]=y(x+1)$, I don't know of any numerical approaches that can handle a problem of that type.
If anyone has any ideas on how this might be solved (or proven unsolvable), they would be appreciated. Thanks!