for: Dynamic Equations on Time Scales: An Introduction With Applications, Birkhauser, Boston (2001) (with Martin Bohner)

• Page 73, Exercise 2.59: $e_{\alpha}(t,0)=\left(\frac{1+\alpha}{e^{\alpha}}\right)^ke^{\alpha t}, quad t\in[2k,2k+1],k\in\N_0.$
• Page 96, after line 23:
\begin{exercise} Solve the following dynamic equations:
\begin{enumerate}
\item $x^{\Delta\Delta}-5x^{\Delta}+6x=0; \item$x^{\Delta\Delta}-6x^{\Delta}+9x=0$; \item$x^{\Delta\Delta}+2x^{\Delta}+2x=0.
\end{enumerate}


• Page 9, After Exercise 1.21:
\begin{exercise} Show that if $f,g:\T\rightarrow\R$ are differentiable,
then
$$(fg)^{\Delta}=\frac{f+f^{\sigma}}{2}g^{\Delta}+\frac{g+g^{\sigma}}{2}f^{\Delta}.$$

Page 64, After Theorem 2.38:
\begin{exercise} Given $\alpha\neq\beta$ are constants with $\frac{\alpha}{t}, \frac{\beta}{t}\in\cR$,
evaluate $\int_{t_0}^t\frac{1}{s+\alpha\mu(s)}e_{\frac{\beta}{t}\ominus\frac{\alpha}{t}}}(s,t_0)\Delta s.$

(i) $y(t)=c_1e_2(t,t_0)+c_2e_4(t,t_0)}+e_3(t,t_0)$.
Part (iii) $y(t)=c_1e_{\frac{4}{t}}(t,t_0)+c_2e_{\frac{1}{t}}(t,t_0)} +\frac{1}{10}e_{\frac{6}{t}}(t,t_0)$.
Page 340 Additional answer to Exercise 3.81 Part (i) $y(t)=c_1e_2(t,t_0)+c_2e_4(t,t_0) -e_3(t,t_0)$.