HELP Taking k 0 and solving the equation about x 0 the cor

HELP!!!

Taking k = 0 and solving the equation about x = 0 the correct to linear independent solutions with x > 0 are: y1 = sigma^infinity_n=0 a_nx^n with a_n = -a_n-2/n^2 y2 = sigma^infinity_n=0 b_nx^n with b_n = a\'_n y1 = x sigma^infinity_n=0 a_nx^n with a_n = -a_n-2/(n+1)^2 y2 = In x y1(x) + sigma^infinity_n=0 b_nx^n with b_n = a\'_n y1 = sigma^infinity_n=0 a_nx^n+r with a_n = -a_n-2/(n + r)^2 y2 = sigma^infinity_n=0 b_nx^n+r with b_n = a\'_n(r) y1 = sigma^infinity_n=0 a_nx^n with a_n = -a_n-2/n^2 y2 = In xy1 + 1+ sigma^infinity_n=0 a_n x^n y1 = sigma^infinity_n=0 a_nx^n with a_n = -a_n-2/n^2 y2 = In xy1 sigma^infinity_n=0 b_nx^n with b_n = a\'_n

Solution

k is not there in the question

there is no condition on a_n wheather it is zero or not.