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Консультация № 187158
10.02.2013, 15:48
167.33 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите решить Обыкновенное дифференциальное уравнение в полных дифференциалах.
primer.docx (14.0 кб)
Желательно с объяснением. Заранее спасибо.
Помогите решить Обыкновенное дифференциальное уравнение в полных дифференциалах.
primer.docx (14.0 кб)
Желательно с объяснением. Заранее спасибо.
Обсуждение
10.02.2013, 16:29
общий
это ответ
Здравствуйте, Пучнин Алексей Александрович!
Так как частные производные совпадают, то уравнение в полных дифференциалах.
Находим общий интеграл:
Взяв
, получим:
В итоге:
Так как частные производные совпадают, то уравнение в полных дифференциалах.
Находим общий интеграл:
Взяв
, получим:В итоге:
Неизвестный
10.02.2013, 18:47
общий
а почему два последних интеграла неопределенные, если в формуле употребляются определенные?
Неизвестный
10.02.2013, 19:08
общий
вроде разобрался. Спасибо. Просто я как то решал и не предовал значения (x0 и y0). Интегрировал с ними.
10.02.2013, 22:49
общий
это ответ
Здравствуйте, Пучнин Алексей Александрович!
Данную задачу можно также решить методом выделения полных дифференциалов. Перегруппировывая слагаемые, получаем
(xdx-ydy)/[$8730$](x2-y2)+(ydx+xdy)+dy/y2=0
d(x2-y2)/2[$8730$](x2-y2)+d(xy)-d(1/y)=0
d[$8730$](x2-y2)+d(xy)-d(1/y)=0
d[[$8730$](x2-y2)+xy-1/y]=0
[$8730$](x2-y2)+xy-1/y]=C
Данную задачу можно также решить методом выделения полных дифференциалов. Перегруппировывая слагаемые, получаем
(xdx-ydy)/[$8730$](x2-y2)+(ydx+xdy)+dy/y2=0
d(x2-y2)/2[$8730$](x2-y2)+d(xy)-d(1/y)=0
d[$8730$](x2-y2)+d(xy)-d(1/y)=0
d[[$8730$](x2-y2)+xy-1/y]=0
[$8730$](x2-y2)+xy-1/y]=C
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