Continuous Functions f(x) Satisfying f(x)>1 and f(x) = x + ∫f(t)dt for All x

[erogol]

Find all continuous functions f(x) satisfying
f(x)>1 and f(x) = x +(1 to x integral) $$\int$$ f(t).dt
for all x

 

[owlpride]

Do you mean

$$f(x) = x + \int_{1}^{x} f(t) dt$$

?

 

[owlpride]

Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.

 

[erogol]

Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.

So i did it but how can i provide the result by this way

 

[erogol]

Do you mean

$$f(x) = x + \int_{1}^{x} f(t) dt$$

?

Yes i mean this integral

 

[John Creighto]

So i did it but how can i provide the result by this way

I'm not sure. Maybe use this:
http://en.wikipedia.org/wiki/Picard–Lindelöf_theorem