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Консультация № 185392
08.02.2012, 22:06
62.88 руб.
0
7
3
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
найти общее решение (общий интеграл) диф.уравнения 1-го порядка y'=(x-y)/(x+y)
найти общее решение (общий интеграл) диф.уравнения 1-го порядка y'=(x-y)/(x+y)
Обсуждение
08.02.2012, 23:24
общий
это ответ
Здравствуйте, Марина!
Делаем замену y=zx
z'x+z=(1-z)/(1+z)
z'x=(1-2z-z2)/(1+z)
(1+z)dz/(1-2z-z2)=dx/x
-0.5ln|1-2z-z2|=ln|x|+C
-0.5ln|1-2(y/x)-(y/x)2|=ln|x|+C
Делаем замену y=zx
z'x+z=(1-z)/(1+z)
z'x=(1-2z-z2)/(1+z)
(1+z)dz/(1-2z-z2)=dx/x
-0.5ln|1-2z-z2|=ln|x|+C
-0.5ln|1-2(y/x)-(y/x)2|=ln|x|+C
Неизвестный
09.02.2012, 00:18
общий
z'x=(1-2z-z2)/(1+z)
(1+z)dz/(1-2z-z2)=dx_
09.02.2012, 07:44
общий
09.02.2012, 07:44
Антон Владимирович! Прочитайте, пожалуйста, свой ответ. В нём неправильно отображаются формулы и имеются ошибки. Предлагаю Вам в мини-форуме консультации поместить отредактированный вариант, чтобы можно было сделать замену. Иначе Ваш ответ придётся удалить.
Об авторе:
Facta loquuntur.
Facta loquuntur.
09.02.2012, 08:45
общий
это ответ
Здравствуйте, Марина!
Заданное уравнение
можно записать так:
Полагая
перепишем уравнение (1) в виде
или
Тогда получим
общий интеграл заданного уравнения.
С уважением.
Заданное уравнение
можно записать так:
Полагая
перепишем уравнение (1) в видеили
Тогда получим
общий интеграл заданного уравнения.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
09.02.2012, 13:16
общий
Два совершенно разных ответа получилось, но оба правильны 
Проверка в Mathcad:
Проверка в Mathcad:
Форма ответа
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