let-g-x-x-1-x-2-1-prove-that-g-is-solution-for-the-differencial-equation-4-1-x-2-y-4xy-y-0-prove-that-g-is-C-on-R-2-determine-a-relation-between-g-n-0-and-g-n-

Question Number 40103 by maxmathsup by imad last updated on 15/Jul/18

l e t g (x) = \sqrt{- x + \sqrt{1 + x^{2}}}

1) p r o v e t h a t g i s s o l u t i o n f o r t h e d i f f e r e n c i a l e q u a t i o n

4 (1 + x^{2}) y^{^{″}} + 4 {x y}^{^{'}} - y = 0 . p r o v e t h a t g i s C^{\infty} o n R

2) d e t e r m i n e a r e l a t i o n b e t w e e n g^{(n)} (0) a n d g^{(n + 2)} (0)