Here is the ODE equation $xy' = 2y$. A book states that the interval where it makes sense doesn't include $0$. Can you explain why? As to me, I think it is defined everywhere.
This problem is from the book "Ordinary Differential Equations - Harry Pollard, Morris Tenenbaum". The exact problem states: "Prove that the functions in the right-hand column below are solutions of the differential equations in the left-hand columns. (Be sure to state the common interval for which solution and differential equation make sense.)"
$xy' = 2y$ and $y = x^2$ with the answer $x \neq 0$