So, I'm trying to solve 2nd order linear differential equations (series solutions near a singular point). (lnx)y" + 0.5y' + y = 0 around the regular singular point x = 1 I got the indicial equation, r(r-0.5) = 0, which leads to the roots.... r1 = 0.5, r2 = 0 The problem only asks us to find the first three nonzero terms in the series y1 = Ʃa_n * (x-1)^r+n from n = 0 to infinity. And we only need to find one solution, corresponding to the larger root. So I took the first and second derivatives of the y1 they gave and plugged it into the differential equation. Now at this point I usually factor out all the x terms. And since the left side has to equal zero for all x, I can divide by that x term to get a recurrence relation (that involves a_n terms). From the relation I can figure out what a_n is. However, in this case, I can't factor out all the x terms because there's a lnx. Anyone know how to get rid of the lnx? Thanks!