求\(f\) 使\(\displaystyle \;f(-x)+\int_{0}^x t f(x-t)dt=x\;(\forall x)\)

elim

题：求所有满足\(\displaystyle \;f\left(-x\right)+\int_{0}^{x}t\cdotp f\left(x-t\right)dt=x\;(\forall x\in\mathbb{R})\)
的\(\mathbb{R}\)上的连续实函数\(\;f.\)