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7.) Two IVPs are given. Call the solution to the first problem y1 (t) and the second yz (t). y" + by' + cy = f (t) + ko(t), y(0)= y'(0)=0 y" + by' + cy = f (t), y (0) = 0,y' (0) = k Show that y1 (t) = y2(t), t > 0, does the solution satisfy the ICs? 8.) Radioactive element X decays to element Y with decay constant Y, in turn, decays to stable 10 element Z with decay constant - -. The functions x (t), y(t), z(t) represents the amount of the elements X, Y, Z, respectively, at time t. If the initial conditions are x (0) = 10, y(0) = 0, z(0) = 0, solve the for x (t), y(t), z(t) subject to the ICs