1. The problem statement, all variables and given/known data Verify that the functions y1(x) = x and y2(x) = 1/x are solutions of the differential equation y'' + (1/x)y' - (1/x2)y = 0 on I = (0,∞). Show that y1(x), y2(x) is a basis of the solution space of the differential equation. 3. The attempt at a solution For the first part I'll just plug the functions back into the differential equation and state the interval in terms of domains, not hard. I'm just confused about how to show the second part. Do I need to show that the two solutions are linearly independent and span the solution space? How do I do this? It's probably simpler than I would think it's just that the language is confusing, mixing linear algebra and differential equations. The general solution would be stated as y(x) = c1y1(x) + c2y2(x). Does this in itself show that the functions form a basis? Since a linear combination of the functions resulted in the solution space? Confusing.