Hello,
An example in a text book I am studying uses the line:
But I can't see how it could be anything other than:
Because can sometimes be a negative value and I can't see how to any exponent could be negative.
Is my way of thinking correct or am I missing something?
Thanks for your time.
From what I understand, at the moment, the problem isn't related to the particular ODE. I think it has more to do with being defined for all real x where as is the inverse for for all . So somehow I have to get my mind around functions that are not one-to-one. This is new ground for me and it doesn't quite make sense yet.
The best I can come up with is that is not just a number with an exponent but is defined (in my texts at least) in terms of being the inverse of that just happens to behave as though it obeys the laws of exponents from algebra.
The example appears to be treating as though it means "inverse of" , so in general what I really need is an understanding of the inverse of which is not a one-to-one function of x.
My brain hurts
Okay this really doesn't belong in this forum but I thought I had better relay what I have found anyway.
It appears that within the example problem the part assumes that the constant of integration from is ignored while evaluating (4). This comes from the derivation of (4) which I shouldn't post here because it is ODE related.
Adding in the constant of integration:
The constant is ignored while evaluating (4) and hence the absolute value vanishes