Write as
The integrating factor is
Integrate:
galactus' (and cyph1e's) solution is much simpler and much shorter, but I think separation of variables in this case is quite instructive:
(or you could keep the -2 with the y's. It makes no difference.)
Now to integrate the left hand side.
Let
So
So
(A is my undetermined constant.)
Now is just a (positive) undetermined constant. Let's call this B.
The way to deal with the absolute value bars is to split this into two equations:
and
Since B is an undetermined (positive) constant anyway, let's say that we can have B be any constant (positive or negative) and just write this as one equation:
-Dan
That is what I thought. That is why I used the integrating factor instead of SOV. Apparently vodka didn't appreciate it, so I deleted it. Last time I answer a question by that poster.but I think separation of variables in this case is quite instructive
I have used my phenomenal cosmic powers to restore galactus' post. My reason is that other users can benefit from seeing the solution if they look up this thread. As I think galactus' solution was not only perfectly acceptable, but efficient and clearly explained I feel it should be included in this thread. (No offense to cyph1e's solution which I think is just as good.)
-Dan