Solutions of Dynamic Equations on Time Scales with Jumps

To obtain the solution of first order dynamic equations on time scales with jumps, a good question to ask is, how many initial conditions will be needed? We shall show that you only need the initial condition that gives you either the initial position or the initial velocity. The solution at each left scattered point in the time scale can be obtained analytically. With this approach we shall write the general form of the solution of a first order dynamic equations on time scales with jumps. To do this we shall use the Hilger derivative, anti-derivatives, the Hilger Complex plane, the exponential function and the cylinder transformation. We shall also use the Marshall Differential Analyzer to obtain the solution of the first order initial value problem as well as calculate the numerical solution to visualize our analytical solution