1.) Suppose T : C C is a linear transformation with the following properties: (a) y1(t) = e2t cos(5t), y2(t) = e2t sin(5t) is a basis of the kernel of T; (b) T[e2t] = 25e2t Use this information to find a solution of the boundary value problem

T[y] = 5e2t, y(0) = 1, y(1) = 0 2

and prove that this solution is unique.