ODDIY DIFFERENSIAL TENGLAMALARGA DOIR IQTISODIY MASALALAR
Keywords:
Differensial tenglama * Differensial tenglama tartibi * Differensial tenglama yechimi * Boshlang‘ich shart * Koshi masalasi * Koshi teoremasi * Umumiy yechim * Umumiy integral * Xususiy yechim * Eng sodda I tartibli differensial tenglama * O‘zgaruvchilari ajralgan tenglama * O‘zgaruvchilari ajraladigan tenglama * Bir jinsli I tartibli tenglama * To‘liq differensialli tenglama * I tartibli chiziqli differensial tenglama * I tartibli chiziqli bir jinsli differensial tenglamaAbstract
Noma’lum funksiyaning hosilalari qatnashgan tenglama differensial tenglama deb ataladi. Differensial tenglamalardan fizika, iqtisodiyot, kimyo, mexanika va boshqa fanlarga doir juda ko‘p masalalarni yechishda keng qo‘llaniladi. Vaqt bilan bog‘liq turli texnologik va iqtisodiy jarayonlar ham matematik usulda differensial tenglamalar orqali tavsiflanadi. Differensial tenglama tartibi unda qatnashgan noma’lum funksiya hosilasining eng katta tartibi bilan aniqlanadi. Differensial tenglamalar yechimining mavjudlik sharti Koshi teoremasi orqali ifodalanadi. Differensial tenglamalar yechimini topish jarayoni uni integrallash deyiladi. Differensial tenglamani integrallashning umumiy usuli mavjud emas. Bundan tashqari juda ko‘p differensial tenglamalarning yechimi elementar funksiyalarda ifodalanmaydi. Shu sababli differensial tenglamalarning ayrim xususiy hollari uchun ularni integrallash usulini ko‘rsatish mumkin. Bu yerda nisbatan soddaroq bo‘lgan I tartibli differensial tenglamalar qaralib, ulardan o‘zgaruvchilari ajralgan, o‘zgaruvchilari ajraladigan, bir jinsli, to‘liq differensialli, chiziqli tenglamalarni va Bernulli tenglamasini integrallash usuli ko‘rsatilgan. Bu tenglamalarni demografiya, marketing va iqtisodiyot masalalarini yechishga tatbiqlari keltirilgan.
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