# Solve the functional equation $f(x+1)-f(x)=x*\sin(x)$ [closed]

Solve $$f(x+1)-f(x)=x*\sin(x)$$

## closed as off-topic by ArsenBerk, Leucippus, YiFan, Sil, ShogunJun 9 at 21:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – ArsenBerk, Leucippus, YiFan, Sil, Shogun
If this question can be reworded to fit the rules in the help center, please edit the question.

• What have you tried so far? – ArsenBerk Jun 9 at 19:46
• @ArsenBerk calculus of finite differences – MorrisonFJ Jun 9 at 19:48

## 1 Answer

Take any function $$f(x)$$ defined on $$[0,1)$$ and then continue to all $$x$$ using the equation.

• Bonus: If $f$ is continuous on $[0,1)$ and $\lim_{x\to1^-}f(x)=f(0)$, then the continuoation will be continuous on all of $\Bbb R$. – Hagen von Eitzen Jun 9 at 20:14
• @HagenvonEitzen but $f(x)=1/4 csc^2(1/2) (sin(x)-x (sin(1-x)+sin(x)))$ . I don't know how to come to this decision – MorrisonFJ Jun 9 at 20:17
• @colt_browning but f(x)=1/4csc2(1/2)(sin(x)−x(sin(1−x)+sin(x))) . I don't know how to come to this decision – MorrisonFJ Jun 9 at 20:30
• @MorrisonFJ Why do you think it's true? Because it's the answer given in the textbook? Well, if this is known to be the correct answer, then the question is apparently missing something. Perhaps the condition that the function must be analytical? This would make the problem a lot harder. – colt_browning Jun 9 at 20:35