The simple mixing tank problem is modelled by the ODE dM M fo cifi dt V(t)' where M (t) is the mass of the substance in the tank, c, is the inflow concentration, f; is the inflow rate, fo is the outflow rate, and V(t) is the volume of the fluid in the tank at time t. (a) Solve this ODE when c = c> 0 is constant, fi = f> 0 is constant, and fi-fo= a > 0 is also constant. Assume that V (to = 0) = Vo.