Tа’rif. Umumiy yechimlar oilasidan ajratib bo’lmaydigan yechimga maxsus yechim deyiladi.
2.O'zgaruvchisi ajralgan differensial tenglama deb qanday t...ga aytiladi
Ushbu M(x)dx+N(y)dy=0 ko’rinishdagi tenglamaga o’zgaruvchilari ajralgan differensial tenglama deyiladi. Uning o’ziga xos tomoni shundaki, dx oldida faqat x ga bog’liq ko’paytuvchi, dy oldida esa faqat u ga bog’liq ko‘paytuvchi turadi. Bu tenglamaning yechimi uni hadma-had integrallash yo’li bilan aniqlanadi:
Misol: xdx+ydy=0 tenglamaning umumiy yechimini toping.
Yechish: Berilgan tenglamani bevosita integrallaymiz natijada
X2/2+ Y2/2=C yoki X2+ Y2=C1 yechimni olamiz.
3.Yechimning mavjudligi haqida teorema keltiring.
Yechimning grаfigi intеgrаl egri chiziq dеyilаdi. Differensial tеnglаmаlаr nаzаriyasidа аsоsiy mаsаlа yechimning mаvjudligi vа yagоnаligidir.
Kоshi tеоrеmаsi. Аgаr funksiya vа uning хususiy hоsilаsi 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