Hi everyone. I'm having a lot of trouble with the idea of a solution to a differential equation HAVING to be paired with an interval in order for it to be considered a solution. So, here's a quick example direcltly from my book...
Solution: Dividing by x, we get the standard form
From this we identify and and further observe that and are continuous on . Hence the integrating factor is
They go on to solve the equation, but my question is why are they justified in dropping the absolute value? It is unclear to me.