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 useLeibnitz ruleto 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.