Find the solution to the initial value problem in explicit form.
I think I screwed up somewhere because when I go to solve for C I get .
The Book's answer in explicit form is
Why does C go in the denominator? I thought that since you are taking the reciprocal of both sides that will just be another constant, C, so I left it alone. It's these types of things that are confusing me, the work is easy but knowing when C gets changed or not is a bit confusing here. Why exactly is C effected here if there is no variable effecting it?
Yeah I screwed up on that part.
My main question is this though, after isolating does it become this: or this: .
I know this is hard to explain but I'll show a link to why I'm a bit confused with the subject of C.
Problem 7 Page 4
If you go to page 4 and problem 7, you can see where he raises both sides to and simply becomes C. So does become here or no? I only ask that because both and are constants, so isn't that the reason why in that problem it is written as ? The math is easy, but working with the C is confusing me with situations like this.
He uses C (upper case) as the original constant and c (lower case) as the 'derived' constant. Therefore, he has c = e^C, where ^ denotes the exponentiation operation.
In your case, you just need to be consistent about which way you use the constant, C, both when you plug-in the initial conditions to solve for C and then when you substitute that value of C back into your expression for y.
You should get the same answer for y either way.