Determine what the value(s) of r has to be in order to find explicit formulas (that is, formulas without integrals) for solutions to . Determine what the general solutions are for each value of .
Just by looking at it, have a few good ones.
Do you see why, say 2, will not work?.
If r=2, then you have an integrating factor of .
Which is not integrable by elementary means.
Actually, are generally not easily integrated.
Trying to integrate can be a booger.
Then you have for r=0
If r=-1, then
And so on. Just something to think about. See if you can find others in the interval that will or will not work.