Consider the pair of functions (y1(t) = e^-2t * cos 5t, y2(t) = e -2t sin 5t). Show that this pair can be a solution of a second order differential equation ay′′ + by′ + cy = 0 and find one such equation.
Consider the pair of functions (y1(t) = e^-t * cos 2t, y2(t) = e -t sin 3t). Show that this pair cannot be a solution of a second order differential equation ay′′ + by′ + cy = 0.