1- find the Laplace transformation to find the v(t) that satisfies the following firs-order differential equation :
a) 500 dv(t)/d(t) +2500 v(t)= 0 , v(-0)= 100V

b) dv(t)/d(t) +200v(t)= 400u(t)V , v(-0)= -100V

2- use the initial and final value properties to find the intial and final values of the waveforms corresponding to the transforms below. if either property is not applicable , explain why ,

a) f1(s)= 16s/((s+2)(s^2+12s+13))

b) f2(s)= (s+10)/(s(s+50)(s+100))

3- a. What are the time constants of the complex poles and the real pole?

b. Which is (are) the "non-dominant" pole(s)? Why?

4- use the initial and final value properties to find the intial and final values of the waveforms corresponding to the transforms below. if either property is not applicable , explain why ,

a) f1(s)= 50(s^2+5s+6)/((s+2)(s+6)(s+12))

b) f2(s)= 10(s^2+10s+40)/((s(s^2 -625))