5. (i) Determine the general solution of the homogeneous ODE, y' + 3y = 0. [5 Marks] (ii) Determine constants ci, c2, c3 such that
5. (i) Determine the general solution of the homogeneous ODE, y' + 3y = 0. [5 Marks] (ii) Determine constants ci, c2, c3 such that Y(x) = car- + cir + co is a particular solution of y' + 3y = 12. (iii) Let Y be any particular solution of Y' + 3Y = x and let y solve the homogeneous initial value problem y' + 3y =0 ly(0) =1 - Y(0). Show that z(x) = y(x) + Y(x) solves the initial value problem z' + 32 =(0) =
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