A differential equation - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: A differential equation ( /showthread.php?tid=867) |

A differential equation - tommy1729 - 05/15/2014
Im a bit rusty on differential equations. I believe this had a solution. Find f such that f ' (x) * x^A = g ( f(x) ) For a nonzero real A and a given entire g(x). In particular g(x) a polynomial. regards tommy1729 RE: A differential equation - tommy1729 - 05/15/2014
Bernouilli differential equations are strongly related ... I intend to use them for tetration. But first I need to think about stuff. regards tommy1729 RE: A differential equation - MphLee - 05/15/2014
I was never able to understand differential equations on wiki (probably because I'm not good with differentials ) but is it a kind of functional equation? Like you have a field with a third operation (i think is called composition algerba) a function and you have to solve( in your case) for the in your case Im getting it in the right way? But is the differentiation operator (or how is called...)? RE: A differential equation - tommy1729 - 05/15/2014
@ MphLee ... mainly ... Here is an example of how I solve the equation with g(x) = x^s where s is some real number. We can rewrite : Let df = f ' (x) and f(x) = f then the equation is equivalent to solving : df f^a = x^b (df f^a)^1/b = x w = f^c dw = c f^(c-1) df (dw)^q = c^q f^(cq - q) (df)^q ... (dw/c)^q = f^(cq -q) (df)^q (dw/c)^1/b = f^((c-1)/b) (df)^1/b ... c-1 = a dw = c x^b dw = (a+1) x^b w = int (a+1) x^b dx + C f = w^(1/c) = w^(1/(a+1)) = ( int (a+1) x^b dx + C )^(1/(a+1)) I think that is correct. I included " ... " to show a different way of thinking has started. I hope that helps. Informally : Integrals and derivatives are used to show how a function behaves for a given function. Differential equations are used to show how behaviour belongs to a function for a given behaviour. regards tommy1729 RE: A differential equation - MphLee - 05/16/2014
I don't want to waste your time explaining me (I should go study the basis) but I don't get some substitutions. You put the value of f(x)=f as and f'(x)=df but what is d? And what is "int(-)"? RE: A differential equation - tommy1729 - 05/16/2014
int just means integral. further df = df/dx regards tommy1729 |