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Консультация № 186763
30.10.2012, 14:25
80.04 руб.
0
4
3
Здравствуйте! Прошу помощи в следующем вопросе:
Решал один из вариантов КР по дифференциальным уравнениям, и столкнулся с тем, что знаю, как решить все уравнения (там только в полных дифференциалах и ЛНДУ), но только одно довел до окончательного ответа (третье), в остальных запутался. Прошу помочь решить данные ДУ: Задание
Ответ крайне желателен до четверга!
Заранее спасибо!
С уважением,
Иван.
Решал один из вариантов КР по дифференциальным уравнениям, и столкнулся с тем, что знаю, как решить все уравнения (там только в полных дифференциалах и ЛНДУ), но только одно довел до окончательного ответа (третье), в остальных запутался. Прошу помочь решить данные ДУ: Задание
Ответ крайне желателен до четверга!
Заранее спасибо!
С уважением,
Иван.
Обсуждение
30.10.2012, 15:03
общий
это ответ
Здравствуйте, Барс Иван!
4
Понижаем порядок путем замены:
Решение полученного линейного уравнения ищем в виде произведения двух функций:
Частное решение ищем так, чтобы выражение в скобках равнялось 0:
4
Понижаем порядок путем замены:
Решение полученного линейного уравнения ищем в виде произведения двух функций:
Частное решение ищем так, чтобы выражение в скобках равнялось 0:
30.10.2012, 16:01
общий
это ответ
Здравствуйте, Иван!
Предлагаю Вам следующее решение первого уравнения. Пусть
Положив
получим 
следовательно, левая часть заданного уравнения - полный дифференциал некоторой функции
т. е.
Проинтегрируем
по 
Найдём функцию
продифференцировав последнее выражение по 
Получаем уравнение
откуда находим
Следовательно, общий интеграл заданного уравнения суть
С уважением.
Предлагаю Вам следующее решение первого уравнения. Пусть
Положив
получим следовательно, левая часть заданного уравнения - полный дифференциал некоторой функции
т. е.Проинтегрируем
по Найдём функцию
продифференцировав последнее выражение по Получаем уравнение
откуда находим
Следовательно, общий интеграл заданного уравнения суть
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Тогда заданное уравнение примет вид
то получим
Форма ответа
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