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Консультация № 189762
11.09.2016, 12:39
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Я застрял на решении дифференциального уравнения, не знаю как дальше двигаться
Я застрял на решении дифференциального уравнения, не знаю как дальше двигаться
Прикрепленные файлы:
Обсуждение
14.09.2016, 16:38
общий
это ответ
Здравствуйте, Посетитель - 399040!
Пусть дано уравнение
Решая это уравнение относительно производной
получим
или
Правая часть уравнения
- однородная функция нулевой степени. Поэтому данное уравнение является однородным. Положим 
тогда 
Подставляя эти значения в уравнение 
получим уравнение с разделяющимися переменными и решим его:
- первый общий интеграл уравнения
Аналогично, решая уравнение
получим второй общий интеграл уравнения 
Если
то уравнение 
принимает вид
откуда либо
либо 
и 
Пусть дано уравнение
Решая это уравнение относительно производной
получимили
Правая часть уравнения
- однородная функция нулевой степени. Поэтому данное уравнение является однородным. Положим тогда Подставляя эти значения в уравнение получим уравнение с разделяющимися переменными и решим его:- первый общий интеграл уравнения
Аналогично, решая уравнение
получим второй общий интеграл уравнения Если
то уравнение принимает видоткуда либо
либо и
Об авторе:
Facta loquuntur.
Facta loquuntur.
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