Tham khảo tài liệu 'handbook ofintegral equations phần 6', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Equations of the Form fa G - dt F x 12. i y t y xt dt A 0 x 1. J0 This is a special case of equation with f t 1 a 0 and b 1. 1 . Solutions y1 x vA y3 x -VÃ y3 x VÃ 3x - 2 y4 x -AA 3x - 2 y5 x AA 10x2 - 12x 3 y6 x -AA 10x2 - 12x 3 . 2 . The integral equation has some other solutions for example AA . AA r . . y7 x 2C 1 x - c - 1 y8 x -- - 2C 1 x - c - 1 c c y9 x vA ln x 1 y10 x -vA ln x 1 where c is an arbitrary constant. 3 . See for some other solutions. 13. i y t y xt dt A 3 0. J0 1 . Solutions y1 x vA y3 x -vA y3 x AB P 2 x - p - 1 y4 x -Ab P 2 x - p - 1 2A where B A AA 2 . The integral equation has some other more complicated solutions of the polynomial n form y x 52 Bk xk where the constants Bk can be found from the corresponding system k 0 of algebraic equations. 14. J y t y xt dt Ax X 0 1 x TO. This is a special case of equation with f t 1 a 1 and b TO. 1 . Solutions y1 x Bx p y3 x X 1 y3 x B 2X - 3 x - 2X 2 x y4 x -B 2X - 3 x - 2X 2 x X 3 where B AA 2X - 1 . 2 . For sufficiently large X the integral equation has some other more complicated solutions n of the polynomial form y x 52 Bkxk where the constants Bk can be found from the k 0 corresponding system of algebraic equations. See for some other solutions. 1998 by CRC Press LLC 15. í e xty t y xt dt A X 0 0 x TO. Jo This is a special case of equation with f t e xt a 0 and b TO. 1 . Solutions y1 x vAX V2 x -VĂX y3 x ỵ 2AX Xx - 2 y4 x -ỵ 2AX Xx - 2 . 2 . The integral equation has some other more complicated solutions of the polynomial n form y x 55 Bk xk where the constants Bk can be found from the corresponding system k 0 of algebraic equations. See for some other solutions. 16. y t y x Xt dt A 0 x TO. 0 This is a special case of equation with f t 1 a 0 and b 1. Solutions y1 x VA y2 x -VÃ y3 x 3A X 1 - 2x y4 x -y 3A X 1 - 2x . 17. y t y x Xt dt A - r A X 3 0 0 x TO. 0 This is a special case of equation with f t 1 a 0 and b TO. Solutions y1 x Aị3 X 1
