IE3

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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\,.


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