Q7. Solve ((0107);) _ 4f{x) = 0 given that f{0) = 2 andf'(0) = 4 (b) 1%) _ 51%) + 6f(X) = 0 given that f(0) = -1 andf'(0) = 0 (c) fa) _ 2f(x) = 0 given that f(0) = 2 Q8. Consider a body falling from a height h, and suppose that it encounters a resistance proportional to its velocity. Show that Newton's equation for this system is dzx _ d_x d1 1 _ mm2 ya: +mg or at +mv g, where y is a frictional coefcient. Solve this equation for v0), given that its velocity at t = 0 is zero. Show that v attains a limiting velocity given by \"um = mg /y. This limiting velocity is called the terminal velocity