How can I solve a differential equation like this one?
$$k \to y(k), \forall k\in[a,b]\subset \mathbb R$$
$$y(k)^2=\int_{k}^{k+\Delta} y'(t)dt$$ where $\Delta$ independent of $k$ has primitive function: $$y(k)^2 = y(k+\Delta)-y(k)$$
This becomes some kind of second degree polynomial equation for each point along the definition space. How to approach it? And maybe more importantly, what are these kinds of equations called if I want to read about them?