Bularni tenglamaga qo‘yib, soddalashtirish natijasida
ko‘rinishdagi kanonik tenglamaga kelamiz. Oxirgi kanonik tenglamani quyidagicha hosil qilish ham mumkin. ni (–2) ga, topilgan xususiy hosilalarning tengliklarini, ya’ni ni 7 ga, Uy ni 4 ga, ni 2 ga, ni 3 ga, ni 1 ga ko‘paytirib, larning oldilaridagi koeffitsientlarni yig‘amiz, natijada
yoki
![](data:image/png;base64,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)
tenglama hosil bo‘ladi. Oxirgi tenglamani (–1) ga ko‘paytirib, kanonik tenglamaga ega bo‘lamiz.
Misol 6: Quyidagi tenglamani kanonik ko‘rinishga keltiring va kanonik tenglamani soddalashtiring.
Yechish: Tenglamaning tipini aniqlaymiz:
bo‘lganligi uchun tenglama elliptik tipga tegishli bo‘ladi va kanonik tenglamasi taxminan
ko‘rinishga ega bo‘ladi. Bunda Q x, y, noma’lum funksiya va uning 1–tartibli hosilalarining funksiyasi bo‘lishi mumkin.
Xarakteristik tenglamasi
bo‘lib, ikkita qo‘shma kompleks
yechimlarga ega. Yangi o‘zgaruvchilar sifatida funksiyalarni belgilaymiz.
funksiyaning xususiy hosilalarini topamiz:
Topilgan ifodalarni tenglamaga qo‘yib, kanonik tenglamaga ega bo‘lamiz:
Bu tenglamani soddalashtirish uchun yangi noma’lum funksiyani kiritamiz:
Hosilalarni hisoblaymiz:
Bu ifodalarni kanonik tenglamaga qo‘yib, soddalashtirish natijasida
tenglamaga ega bo‘lamiz. va sonlarni bo‘ladigan qilib tanlaymiz. U holda ;
bo‘lib, soddalashtirilgan kanonik tenglama
ko‘rinishga ega bo‘ladi.
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