please provide detailed step

B.2 Assume that an engineering system can either be in the three states: i = 0 (operating normally), i = 1 (failed due to hardware problem), or i = 2 (failed due to human errors). The following set of differential equations describes the probability (X; (t) ) that the engineering system is in state i at time t (in hours) where i = 0, 1,2: dx (t) + 0.005X.(t) = 0 dt dx, (t) 0.004X.(t) = 0 dt dX2 (t) 0.001X. (t) = 0 dt At the initial time, we know that the engineering system is operating normally. Apply Laplace Transform to solve the engineering problem and find out the mean time to system failure, MTTF = S. Xo(t)dt