IE3

Find lambda: $y(x)=\lambda\int_0^1 y(t)dt\,$ if $y(x)=c\,$

If $y(x) = c\,$ , then

$y(x)=\lambda\int_0^1 y(t)dt\,$	$\Longrightarrow c = \lambda\int_0^1 c\ dt\,$
	$\Longrightarrow c = c\lambda\int_0^1 dt\,$
	$\Longrightarrow c = c\lambda\left(t\left.\right\|_0^1\right)\,$
	$\Longrightarrow c = c\lambda\,$

Therefore, $c = 0\,$ or $\lambda = 1\,$ .