Week Six Topic: Reduction of Order Give a convincing demonstration that the second-order equation (0.1) ay + by + cy = 0 where a, b and c are constants, always possesses at least one solution of the form y1 = em1x , m1 a constant. Also, explain why the differential equation in (0.1) must then have a second solution either of the form y2 = em2x or of the form y2 = xem1x , m1 and m2 constants. 1