6. Suppose that y(t) satisfies the differential equation y"(t) + 5y" (t) + 6y' (t) = 2e t with y(0) = -2, y'(0) = 6 and y" (0) = -14. If z(t) = y(t), find a differential equation for z(t) and the values of z(0) and z'(0). Hence find z(t). Use this to find y(t).