g is real function continue let f(x)=∫_0 ^x sin(x−t)g(t)dt 1)prove that f^′ (x)= ∫_0 ^x cos(t−x)g(t)dt 2)prove that f is so<ution of the diff.equa. y^(′′) +y =g(x)


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Question Number 31507 by abdo imad last updated on 09/Mar/18

$g i s r e a l f u n c t i o n c o n t i n u e l e t$ $f (x) = \int_{0}^{x} s i n (x - t) g (t) d t$ $1) p r o v e t h a t f^{^{'}} (x) = \int_{0}^{x} c o s (t - x) g (t) d t$ $2) p r o v e t h a t f i s s o < u t i o n o f t h e d i f f . e q u a .$ $y^{^{″}} + y = g (x)$
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