Yechish: Berilgan sistemaga mos bir jinsli sistema tuzib olamiz
Bu sistemaga Eyler usulini qo’llaymiz
ko’rinishdagi xususiy yechimni izlaymiz:
Bu ifodani (*) ga qo’yamiz:
Bu sistemaga mos harakteristik tenglama tuzamiz:
harakteristik tenglama
uchun α , β larni izlaymiz:
xususiy yechim.
uchun α , β larni izlaymiz:
xususiy yechim.
Demak mos bir jinsli sistemaning umumiy yechim ko’rinishi quyidagicha:
Endi bundan sistemaning umumiy yechimini topamiz:
Buning uchun mos bir jinsli sistemaning umumiy yechimidan foydalanamiz:
Bunga varriatsialash usulini qo’llaymiz:
deb olamiz. Bundan
endi hosilalarini olamiz:
Demak
![](data:image/png;base64,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)
Bu sistemadan va larni topamiz.
Integrallaymiz:
va larni (**) ga olib borib qo’yamiz.
Bu berilgan sistemaning umumiy yechimi.
Do'stlaringiz bilan baham: |