6-MAVZU. AMALIYOT
CHIZIQLI OʻZGARMAS KOEFFITSIYENTLI YUQORI TARTIBLI BIR JINSLI DIFFERENSIAL TENGLAMALAR.
Misol. Quyida berilgan chiziqli oʻzgarmas koeffitsiyentli yuqori tartibli bir jinsli differensial tenglamalar yechilsin:
Xarakteristik tenglamasi:
u holda yechim: koʻrinishda boʻladi
Xarakteristik tenglamasi: ![](data:image/png;base64,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)
u holda yechim: , konstantalar.
Xarakteristik tenglamasi:
u holda yechim:
,
konstantalar.
Agar xarakteristik tenglama ildizlari:
yechim
yechim
yechim
– qoʻshma kompleks ildiz boʻlsa
– qoʻshma kompleks ildiz boʻlsa
m-karrali qoʻshma kompleks ildiz boʻlsa, u holda unga mos umumiy yechim
koʻrinishda boʻladi, -konstantalar
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