Abel's theorem

Theorem

Let $t_0 \in \mathbb{T}^{\kappa}$ and assume $y^{\Delta \Delta}(t) + p(t) y^{\Delta}(t) + q(t)y(t) = 0$ is regressive, where $p$ and $q$ are rd continuous. Suppose that $y_1$ and $y_2$ are two solutions of $L_2 y=0$. Then their Wronskian satisfies $$W(t) = e_{-p+\mu q}(t,t_0)W(t_0)$$ for $t \in \mathbb{T}^{\kappa}$, where $e_{-p+\mu q}$ denotes the delta exponential.