State which of the following problems are under-determined (that is, have insufficient boundary conditions to determine all the arbitrary constants in the general solution) and which are fully determined. In the case of fully determined problems state which are boundary-value problems and which are initial-value problems. (Do not attempt to solve the differential equations.)

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dx (a) 4x- + dt (b) (c) (d) (e) da dt X dx + ( 2 - 1) d x dt dx dt x(0) = 0, N +1- dx X dfdt +4- dx dt dx dax dt4 x(0) = 1, x(2) = 0 dx dt dx dt -(0)= 1, x(2) = 0 (0) - x = sint, x(0) = a - 4xt = 0, x(0) = 4 0 = dx dx dt dt + - 4x = e' d.x 2t- =t-4, x(0) = 1, x(2) = 0 dt