tartibini pasaytirish mumkin bo‘lgan yuqori tartibli differensial tengl

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oddiy differentsial tenglamalar reja: 1. . ko’rinishdagi differensial tenglamalar. 2. ko’rinishdagi differensial tenglamalar. 3. (erkli o’zgaruvchi oshkor qatnashmagan) ko’rinishdagi differensial tenglamalar. (1) (2) tartibini pasaytirish mumkin bo’lgan yuqori tartibli differensial tenglamalarning ba’zi turlarini ko’rib shiqamiz. i. ko’rinishidagi differensial tenglamalar (1) (2) (3) misol: differensial tenglamani yeshing. (3) (4) echish: ii. ko'rinishidagi differentsial tenglama. yoki (1) (2) (3) (4) (5) iii. x erkli o'zgaruvchini oshkor holda o'z ichiga olmagan differentsial tenglama (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) e’tiboringiz uchun raxmat ( ) ( ) 0 ,.... , , , ' ' ' = n y y y y x f ( ) ( ) 1 ()''' ,,,,..., n n yfxyyyy - = ( ) ( ) x f y n = ( ) ' ()(1) nn yy - = (1) 1 () n yfxdxc - =+ ò ( ) (2) 12 () n yfxdxdxcxc - =+×+ òò …

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salasini yechamiz : 0  x bo’lganda 0 , 0    y y bo’lganligi uchun , . 4 1 , 0 , 0 0 sin 2 1 0 0 0 cos 4 1 2 1 1 2 1          c c c c c sh unday qilib , koshi masalasining yechimi 4 1 2 cos 4 1    x y bo’ladi . 2 2 , dydy fx dxdx æö = ç÷ èø ( ) ''' ,,0 fxyy = dy p dx = 2 2 dydp dxdx = (,) dp fxp dx = 1 (,) ppxc = dy p dx = 12 (,) ypxcdxc =+ ò 2 2 , dydy fy dxdx æö = ç÷ èø ( ) ''' ,,0 fyyy = dy p dx = 2 2 dydpdpdydp p dxdxdydxdy ==×=× û (,) dp pfyp dy ×= 1 …

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dy 1 2 2 1   bo’ladi . oxirgi tenglikdan 2 1 2 1 1 1 c x c y yoki c x c y       bo’ladi . bu berilgan tenglamaning umumiy yechimi bo’ladi .

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oddiy differentsial tenglamalar reja: 1. . ko’rinishdagi differensial tenglamalar. 2. ko’rinishdagi differensial tenglamalar. 3. (erkli o’zgaruvchi oshkor qatnashmagan) ko’rinishdagi differensial tenglamalar. (1) (2) tartibini pasaytirish mumkin bo’lgan yuqori tartibli differensial tenglamalarning ba’zi turlarini ko’rib shiqamiz. i. ko’rinishidagi differensial tenglamalar (1) (2) (3) misol: differensial tenglamani yeshing. (3) (4) echish: ii. ko'rinishidagi differentsial tenglama. yoki (1) (2) (3) (4) (5) iii. x erkli o'zgaruvchini oshkor holda o'z ichiga olmagan differentsial tenglama (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) e’tiboringiz uchun raxmat ( ) ( ) 0 ,.... , , , ' ' ' = n y y y y x f ( ) ( ) 1 ()''' ,,,,..., n n yfxyyyy - = ( ) ( ) x …

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