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Kisuni
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Вот такое задание.
Перевела в полярные координаты, разделила переменные получилось два уравения:
p^2*R''+p*R-kR=0 (1)
Ф''+kФ=0
Решаю второе урафнение с начальными условиями:
Ф(0)=0
Ф'(2П/3)=0
Получаю:
Ф=Аcos(sqrt(k)fi)+Bsin(sqrt(k)fi)
Ф(0)=0 => А=0
Ф=Bsin(sqrt(k)fi)
Ф'=sqrt(k)*Bcos(sqrt(k)fi)
Ф'(2П/3)=0 => cos(2П/3*sqrt(k))=0
2П/3*sqrt(k)=П/2+Пn
Отсюда k=((3+6n)/4)^2
Ф=Bsin((3+6n)/4*fi)
Дальше ищем функию R в виде R=p^m
Подставляем в (1), получаем m(m-1)+m-((3+6n)/4)^2=0, получаем
m=(3+6n)/4
Получаем, что u=Сумма(Bn*sin((3+6n)/4*fi)*p^((3+6n)/4)
учитывая начальное условие u(1,fi)=5*sin(3*fi)=Сумма(Bn*sin((3+6n)/4*fi))
Получается, что (3+6n)/4=3, значит n=3/2.
Но n же целое быть должно! Не могу найти ошибку в расчетах. Помогите, пожалуйста.
wils
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wils
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