Well, the most obvious reason would be to verify that without these we still get a solution to the DE (besides you do want to get rid of them because they threaten the differentiability of the solution).
Hi, can someone explain to me the process of dealing with the absolute value signs in this problem:
Solve the given initial value problem and give the largest interval on which the solution is defined.
So, I get to this point: .
Now, how do I deal with these absolute values, and what is the justification for dropping them? WolframAlppha gives
So, what about going this route...
But, is of the form and we are only seeking a solution on an interval for which the coefficient function is continuous. So, we take and therefore we are justified in removing the absolute value signs, giving
What about that? Page 53. Right under equation (2).