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$\begingroup$

Take an equation

$$w'+w-w^2-1=0$$

Its solution is

$$w(x)=\frac{\sqrt{3}}{2} \tan \left( \frac{\sqrt{3}}2 C+\frac{\sqrt{3}}2 x\right)+\frac12$$

I wonder why a similar difference equation

$$\Delta w+w-w^2-1=0$$

cannot be solved?

  • 0
    I think I would first ask why is there a nice formula for $\int\sqrt x\,dx$ but not for $\sum\sqrt n$.2012-08-10
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    @Gerry Myerson there is such formula. http://en.wikipedia.org/wiki/List_of_derivatives_and_integrals_in_alternative_calculi http://en.wikipedia.org/wiki/Indefinite_sum2012-08-10
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    Why would there be any implication between the easy solvability of one and of the other/2012-08-10
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    Anixx, you and I have different opinions as to what constitutes a "nice" formula.2012-08-10

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