Consider the following first order differential equation x =ax+bu where a = -2, b=10, u(t)=e-2t and the initial condition is x(o)=5. (1) determine the analytic solution of this differential equation by identifying the expression x(t). (ii) calculate x(t) at t=0.5. (ii) using the explicit euler method with a sample time of 0.25, determine the discrete-time model xx+1=47**+ (iv) calculate xt for the time corresponding to t=0.5.