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Question Number 30215 by abdo imad last updated on 18/Feb/18

l e t g i v e J (x) = \frac{1}{π} \int_{0}^{π} c o s (x c o s t) d t

1) f i n d J^{^{'}} a n d J^{^{″}} i n f o r m o f i n t e g r a l s

2) p r o v e t h a t J^{^{'}} (x) = \frac{- x}{π} \int_{0}^{π} {s i n}^{2} t c o s (x c o s t) d t a n d J i s

s o l u t i o n o f d . e . {x y}^{^{″}} + y^{^{'}} + x y = 0