Related to differential equations

I have found a solution to a DE which is y = (9/13)Ae^(-2x)+(4/13)Acos(3x)+(19/39)Asin(3x). where A is a parameter family of solutions. So my graph consists of a= -.5 through 2.5, using intervals of .5. In the graph, these 7 curves intersect (i think because of the cos and sin function) every pi/3 along the x-axis. Why does this not contradict the uniqueness theorem for linear differential equations?