0
$\begingroup$

$$ f(x)= \int_0^1 e^{|x-t|} f(t) \, dt+x-1 $$

I can't solve it, because I can't find the boundary conditions?

  • 0
    Normally, one uses an iterative technique to solve this. Just start iterating using $x-1$.2011-12-17
  • 0
    Thank you for your comment, however in this exercise I have to use this method (using eigen values) to solve it. Do you know how I can do it?2011-12-17
  • 0
    This is quite interesting as you can consider your integral a linear operator and compute $∫_0^1e^{|x-t|} u(t)dt=\lambda u(x)$. Looking at the answer by Didier, this just becomes $$\lambda u''(x)=3u(x).$$ Taking $\lambda=1$ you are back to the proposed answer.2011-12-17

3 Answers 3