Handbook of mathematics for engineers and scienteists part 208

Handbook of mathematics for engineers and scienteists part 208. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Linear Functional Equations in One Independent Variable 1417 . Linear equations involving unknown function with rational argument. x a - x 34 y x - y . 1 bx Solution x J a-x A y x I x - V 1 bx where x z z x is any symmetric function with two arguments. i a - x 35. y x y 1 bx Solution X J a-x A y x x - 1 bx where x z - z x is any antisymmetric function with two arguments. i a - x _z x 36. y x yÇ 1 X f x . a_x 1J. Solution y x 2f x Wx V 1 bx where x z - z x is any antisymmetric function with two arguments. x a - x 37. y x - ni f x . Here the function f x must satisfy the condition f x -f Solution a _ x 1 bx y x 2 f x x a _ x 1 bx where x z z x is any symmetric function with two arguments. 38. y x - cy f x c 1. 1 bx z Solution . . 1 . c f a_x y x 7 f x 7 d TTj l- 39. y x g x y - -i f x . 1 bx Solution x f x _ 9 x f z y 1 _ g x g z a_x 1 bx ax - Q x 40. y x c ------- f x x b J A special case of equation . ß a2 ab b2. 1418 Functional Equations 41. y x cy bx 3 a - x f x 3 a2 ab b2. A special case of equation . rax - 3 . 42. y x g x y ------ f x x b A special case of equation . i bx 3 . 43. y x g x y --- f x a-x 3 a2 ab b2. 3 a2 ab b2. A special case of equation . . Linear functional equations involving y x and y Va2 - x2 . 44. y x - y Va2 - x2 0 0 x a. Solution _ y x x V a2 - x2 where x z z x is any symmetric function with two arguments. 45. y x y Va2 - x2 0 0 x a. Solution _ y x x V a2 - x2 where x z - z x is any antisymmetric function with two arguments. 46. y x y Va2 - x2 b 0 x a. Solution q ifwA h-L- b w a ct2 cf 2 A y x 2U x v a x j where x z - z x is any antisymmetric function with two arguments. 47. y x y Va2 - x2 f x 0 x a. Here the function f x must satisfy the condition f x f Va2 - x2 . Solution Q IiwA J- f i rpA i lb W A Ct 2 cf 2 A y x 2 f x w x v a x j where x z - z x is any antisymmetric function with two arguments. 48. y x - y Va2 - x2 f x 0 x a. Here the function f x must .