I'm posting this under analysis because of the method I'm thinking about using to solve it.(adsbygoogle = window.adsbygoogle || []).push({});

Here is the equation:

[tex]\varepsilon \left( x\right) =e^{\varepsilon \left( x-1\right) }[/tex]

and the initial condition is

[tex]\varepsilon \left( 0\right) =1[/tex].

My main goal is to consider x as a number in [0,1] but we can start with x being a natural number.

Here's what I want to try now. I'm pretty sure [tex]\varepsilon[/tex] is not elementary so let's assume it's of the form

[tex]\varepsilon \left( x\right) =\int_{0}^{\infty }f\left( t,x\right) dt[/tex].

Now my question is how do i solve for f?

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# A nonlinear difference equation

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