4. 5. Determine the initial and final values of the function f(t) whose Laplace transform is: F(s) = 2 (s+7s+15s) Determine the steady state value of the function whose Laplace transform is: 4s+5s+6 s(2s3+7s+13s+2) 6. For the following differential equations and initial conditions, write the transforms of the solutions (i.e. determine the s-domain solutions): (a) 6c+13c = 5u(t); c(0) = 1, (0) = 4 (b) + 3+ 4c = 6sinwt; c(0) = 4, (0) = 5 (c) +2c4c = u(t); c(0) = 1, (0) = 0 (d) y + y = 0; == y(0) = y(0) = 0, y(0) = 5 dt4 dt d40 d30 (e) + d20 +6 dt de +12 +0 = (1 + sint)u(t) dt zero initial conditions.