chiziqli differensial tenglamalar sistemasi

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oddiy differensial tenglamalar 30-mavzu. chiziqli differensial tenglamalar sistemasi differensial tenglamalar sistemasi tenglamalar sistemasini yechimi deb 1-tartibli uzluksiz hosilaga ega bo`lib, tenglamalar sistemasini ayniyatga aylantiradigan har qanday funksiyalarga aytiladi. differensial tenglamalar sistemasi uchun koshi masalasi deb boshlang`ich shartlarni qanoatlantiruvchi tenglamalar sistemasining yechimiga aytiladi. sistemaning yechimini toping. xarakteristik ildizlarni topamiz: demak, sistemaning yechimini quyidagi ko`rinishda izlash mumkin: u holda sistemadagi 1-tenglamadan quyidagini hosil qilamiz: shunday qilib sistemaning umumiy yechimi: ( ) ( ) ( ) 1 112 2 212 12 ,,,...,, ,,,...,, ................................... ,,,...,. n n n nn dy fxyyy dx dy fxyyy dx dy fxyyy dx ì = ï ï ï = ï í ï ï ï = ï î ( ) ( ) ( ) 000 1012020 ,,..., nn yxyyxyyxy === ( ) ( ) ( ) 1122 ,,..., nn yxyxyx jjj === ( ) ( ) ( ) 1122 ,,..., nn yxyxyx jjj === 1 11111 2 21122 11 …
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oddiy differensial tenglamalar 30-mavzu. chiziqli differensial tenglamalar sistemasi differensial tenglamalar sistemasi tenglamalar sistemasini yechimi deb 1-tartibli uzluksiz hosilaga ega bo`lib, tenglamalar sistemasini ayniyatga aylantiradigan har qanday funksiyalarga aytiladi. differensial tenglamalar sistemasi uchun koshi masalasi deb boshlang`ich shartlarni qanoatlantiruvchi tenglamalar sistemasining yechimiga aytiladi. sistemaning yechimini toping. xarakteristik ildizlarni topamiz: demak, sistemaning yechimini quyidagi ko`rinishda izlash mumkin: u holda sistemadagi 1-tenglamadan quyidagini hosil qilamiz: shunday qilib sistemaning umumiy yechimi: ( ) ( ) ( ) 1 112 2 212 12 ,,,...,, ,,,...,, ................................... ,,,...,. n n n nn dy fxyyy dx dy fxyyy dx dy fxyyy dx ì = ï...

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