6. Answer each question separately. Justify your answers. (a) Let k be a real constant. It is known that y = e" sin (2x) is a solution to the differential equation y" - 2y' + ky = 0. Find the possible value(s) of k. (b) Let C be the curve defined by er + y + sin(2xy) = 2. The point (0, 1) is on the curve C. Find the equation of the tangent line to the curve C at (0, 1). (c) By considering the function f(x) = In x and using Lagrange's mean value theorem on 1, - , show that 1 11