Abel dynamic equation

Let $\mathbb{T}$ be a time scale and let $f_i,g_k \colon \mathbb{R} \rightarrow \mathbb{R}$ for $i=0,1,2$ and $k=0,1$. The Abel dynamic equation of the second kind is $$\left[ g_0(x)+g_1(x) \left( \dfrac{u+u^{\sigma}}{2} \right) \right]u^{\Delta} = f_0(x)+f_1(x)u+f_2(x)u^2.$$

References

Abel dynamic equations of the first and second kind