1. The problem statement, all variables and given/known data The problem and its answers are attached. I prefer the first one as (same thing but isolated for y): y_1(x) = [k_1 * x + x * ln(x)]/[k2 - ln(x)] 2. Relevant equations First order homogeneous differential equation. y = xv, dy/dx = v + x dv/dx 3. The attempt at a solution I solved this successfully. Given that at some point in the solution of the problem for solving y_1(x), I get a denominator with (x+y), it is my "mathematical duty" to check if x + y = 0 => y = -x is a solution to the differential equation and it is. Because of the nature in which I got this y = -x solution, I am confused as to whether I treat this as one of the two alternatives for a general solution or both together span the one and only general solution. Any input would be greatly appreciated! Thanks in advance!