A problem to be solved using integration by parts. – math.stackexchange.com

Assume all functions of the form $(0,1)\to\mathbb{R}$. Given that $$ f(x) - \lambda_1 f''(x) = 0 $$ and $$ g(x) - \lambda_2 g''(x) = 0, $$ for all $x \in (0,1)$. Also, $$ f(0) = f(1),\qquad f'(0) = ...

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