Hi everyone, name is Ryan. This is my first post here, seems like a very beneficial forum. I look forward to being helped and helping others. Anyway I'm trying to teach myself Implicit Differentiation but there doesn't seem like much useful resources online and I don't quite understand it.
I'm trying to produce a degree 3 polynomial for (dy/dx) = 1/(3y^2); y(0)=1 using implicit differentiation.
The Attempt at a Solution
Alright I started off by trying to find (d^2)y/d(x^2) and this is how I did it:
(d^2)y/d(x^2) = -6/[y(0)^3] x [(dy/dx)](0)
= -6x1x(1/3) = -2
Now to get (d^3)y/d(x^3) I get a bit confused, as well as just getting y.
I tried getting (d^3)y/d(x^3) as follows:
(d^3)y/d(x^3) = 18/[y^4] x [(d^2)y/d(x^2)](0)
= -18 x1x-2 = 36 (I suspect this is wrong)
And I have no idea how to get y. If someone has any idea how to di is or just some tips that would be much appreciated. Thanks guys.