I'm having a diffucult time sovling this problem The problem statements reads as.
x = y(x) - (1/2)*integral( (1-|x-u|) * y(u) du) from -1 to 1.
From direct differentialtion, we are suppose to use Leibnitz rule to prove that
y''(x) + y(x) = 0,
subject to
y(1) + y(-1) = 0
and
y'(1) + y'(-1) = 2
Any help would be appreicated. Differentiating the absolute value of (x-u) with respect to x is giving me issues.
Thank you.