chiziqli differentsial tenglamalar

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1714506273.pptx ta’rif. no’malum funksiya va uning hosilasi birinchi darajada bo’lgan birinchi tartibli differensial tenglamaga chiziqli differensial tenglama deyiladi. 0)()(')(  xcyxbyxa (1) dan iborat. bunda )(),(),( xcxbxa ko’rilayotgan oraliqda uzluksiz funksiyalardir. agar ko’rilayotgan oraliqda ning hamma qiymatlarida 0)(xa bo’lmasa, (1) tenglamani )()(' xqyxpy  (2) )( )( )(, )( )( )( xa xc xq xa xb xp  (2) tenglamaga bir jinsli bo’lamagan chiziqli differensial tenglama deyiladi. 0 ) ( ) ( ' ) ( = + + x c y x b y x a ) ( ), ( ), ( x c x b x a 0 ) ( ¹ x a ) ( ) ( ' x q y x p y = + ) ( ) ( ) ( , ) ( ) ( ) ( x a x c x q x a x b x p - = = ta’rif. no’malum funksiya va uning …

i. (2) tenglamaning ham umumiy yechimini quote ni ning funksiyasi deb, (4) ko’rinishda izlaymiz. _1738493556.unknown _1738493883.unknown _1738493555.unknown u holda (4) dan      dxxpdxxp xpxcxcy )()( )()()(''  (5) (4) va (5) ga asosan (2) tenglama )()(')()(' )()()()()()(' )()( )()()( xqxcxqxc xqxpxcxpxcxc dxxpdxxp dxxpdxxpdxxp              ò - ò = - - dx x p dx x p x p x c x c y ) ( ) ( ) ( ) ( ) ( ' ' l l ) ( ) ( ' ) ( ) ( ' ) ( ) ( ) ( ) ( ) ( ) ( ' ) ( ) ( ) ( ) ( ) ( x q x c x q x c x q x p x c x p x c x c dx x p dx …

own _1738494952.unknown (2) tenglamaning umumiy yechimini eyler -bernulli usulidan foydalanib topish ham mumkin. (2) tenglamada uy (8) almashtirishni olamiz. bunda va lar ixtiyoriy uzluksiz differensiallanuvchi funksiyalardir. ''' uuy  )()('' xquxpuu   (9) )())('(' xquxpuu   (10) funksiya ixtiyoriy bo’lgani uchun, uni shunday tanlab olamizkim j u y = ' ' ' j j u u y + = ) ( ) ( ' ' x q u x p u u = + + j j j ) ( ) ) ( ' ( ' x q u x p u u = + + j j (2) tenglamaning umumiy yechimini eyler-bernulli usulidan foydalanib topish ham mumkin. (2) tenglamada (8) almashtirishni olamiz. bunda va lar ixtiyoriy uzluksiz differensiallanuvchi funksiyalardir. (9) (10) funksiya ixtiyoriy bo’lgani uchun, uni shunday tanlab olamizkim _1738493566.unknown _1738493567.unknown _1738493568.unknown _1738493565.unknown 0)(' uxpu sharti bajarilsin. bundan dxxp u du )(    dxxp udxxpun …

ntsial tenglamalar re’ja chiziqli differensial tenglamalar haqida maʼlumot. bir jinsli differentsial tenglamalar. bernulli usuli yordamida tenglamalarni xisoblash. e`tiboringiz uchun tashakkur!!! image1.emf oleobject1.bin image2.emf oleobject2.bin image3.emf oleobject3.bin image4.emf oleobject4.bin image5.emf oleobject5.bin image6.emf oleobject6.bin image7.emf oleobject7.bin image8.emf oleobject8.bin image9.jpeg image10.jpeg

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1714506273.pptx ta’rif. no’malum funksiya va uning hosilasi birinchi darajada bo’lgan birinchi tartibli differensial tenglamaga chiziqli differensial tenglama deyiladi. 0)()(')(  xcyxbyxa (1) dan iborat. bunda )(),(),( xcxbxa ko’rilayotgan oraliqda uzluksiz funksiyalardir. agar ko’rilayotgan oraliqda ning hamma qiymatlarida 0)(xa bo’lmasa, (1) tenglamani )()(' xqyxpy  (2) )( )( )(, )( )( )( xa xc xq xa xb xp  (2) tenglamaga bir jinsli bo’lamagan chiziqli differensial tenglama deyiladi. 0 ) ( ) ( ' ) ( = + + x c y x b y x a ) ( ), ( ), ( x c x b x a 0 ) ( ¹ x a ) ( ) ( ' x q y x p y = + ) ( ) …

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