So I learned about these equations in my math class this spring, and it has been bothering me for some time that you are able to merely drop the offending term when there is overlap in the solutions. A quick example might help, seeing as I don't really know the true terms. When finding the general solution for y''-2y'=x+2e^2 you end up with an overlap in yh and yp of Ce^x, and so when bringing it together you just ignore one of them. Why is this a legitimate thing to do? Why does it not violate any rules? I tried to figure it out myself using the above equation and multiplying the two equations through by x, resulting in xyh+xyp=(C1x+C2xe^2x)+(Ax^2+Bx+Cxe^x). Not to bore you with the particulars, but it resulted in x=x, which of course tells me nothing. Can someone please enlighten me?