I'd like to know the solution (if solvable) to the following integral equation $$f(x) - \int_0^x f(t)dt = 0$$ Also I'd like to know what is the required mathematical background to be able to find a solution to this kind of equations by myself, I'm studying some topology at the moment and have studied calculus (single and some multivariable) and ordinary differential equations...so how far am I to begin solving integral equations?
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2Can you solve $\frac{d}{dx}F(x) - F(x) = 0$? – Michael Biro Nov 23 '14 at 04:41
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2Is it $\displaystyle{{\rm f}\left(, x,\right) - \int_{0}^{x}{\rm f}\left(, t,\right),{\rm d}t = 0}$ ?. – Felix Marin Nov 23 '14 at 04:42
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K*e^x (K real)......thanks!!! i didn't notice it – Rodney Velis Nov 23 '14 at 04:47
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1wait, that's a solution to the differential equation .....not to the integral because of the K – Rodney Velis Nov 23 '14 at 04:49
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1Does it not imply then that K=0 and therefore $f(x)=0$ – Rammus Nov 23 '14 at 04:52
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Yes Peter Brown ... thanks – Rodney Velis Nov 23 '14 at 04:57
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Yes Felix Martin...it is $f(x) - \int_0^x f(t)dt = 0$, sorry for the late response and for the mistake – Rodney Velis Nov 23 '14 at 04:58
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Can someone suggest me a good book to learn to solve integral equations?....if you think i'm still not able to study the topic, tell me what else do i need to know or other required background – Rodney Velis Nov 23 '14 at 05:09
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1The integral equation in this question is a very special case of one that can be reduced to a differential equation. More general integral equations, like Fredholm or Volterra equations, are probably out of your reach until you're much more experienced with analysis, at least up to functional analysis. – Gyu Eun Lee Nov 23 '14 at 05:24