Timeline for Solution of certain forms of equations

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when toggle format	what		by	license	comment
Nov 19, 2012 at 20:14	comment	added	Safwane		Ok, Thank you very much. I will try to do this.
Nov 19, 2012 at 19:29	comment	added	Robert Israel		If you want a series solution, you'll want to expand around a known solution in powers of some parameter. Thus suppose you write your equation as $F(w) - \epsilon G(w) = 0$, where $F$ and $G$ are analytic, and $F(0) = 0$ so that $w = 0$ is a solution when $\epsilon = 0$, while $G(0) \ne 0$ and $F'(0) \ne 0$. Then the Lagrange inversion theorem gives a series expansion for $w$ in powers of $\epsilon$, convergent for sufficiently small $\epsilon$.
Nov 19, 2012 at 19:07	history	edited	Robert Israel	CC BY-SA 3.0	edited body
Nov 19, 2012 at 17:35	comment	added	Safwane		What about the case where $a,b,c,x,y$ are real valued functions on certain w (the unknown variable) and $n$ is a fixed integer.
Nov 19, 2012 at 17:24	vote	accept	Safwane
Nov 19, 2012 at 17:16	history	answered	Robert Israel	CC BY-SA 3.0