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-lt-ution-of-the-diff-equa-y-y-g-x-

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)