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Консультация № 191977
03.12.2017, 19:01
0.00 руб.
1
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Найти частное решение с неопред.коэф.
y''+6y'+10y=3xe^(-3x)-2e^(3x)sinx
Найти частное решение с неопред.коэф.
y''+6y'+10y=3xe^(-3x)-2e^(3x)sinx
Прикрепленные файлы:
Обсуждение
09.12.2017, 11:43
общий
это ответ
Здравствуйте, Inna!
Пусть требуется вычислить частное решение уравнения
Рассмотрим сначала уравнение
Составим и решим его характеристическое уравнение.
Фундаментальную систему решений уравнения
составляют функции
Общее решение уравнения имеет вид
где
определяются по формулам 
Для решения задачи воспользуемся методом Лагранжа, положив, что частное решение уравнения
имеет вид
где определяются по формулам
Получим
Вам остаётся вычислить первообразные, выполнить необходимые преобразования и получить ответ на заданный вопрос, учитывая формулу
Перед этим проверьте правильность моих предыдущих расчётов, потому что я не могу гарантировать их безошибочность.
Можно, разумеется, поступить иначе. Для этого воспользуйтесь тем, что если
и 
-- частные решения соответственно уравнений
и
то функция
является частным решением уравнения 
Пусть требуется вычислить частное решение уравнения
Рассмотрим сначала уравнение
Составим и решим его характеристическое уравнение.
Фундаментальную систему решений уравнения
составляют функцииОбщее решение уравнения
имеет видгде
определяются по формулам Для решения задачи воспользуемся методом Лагранжа, положив, что частное решение уравнения
имеет видгде
определяются по формулам Получим
Вам остаётся вычислить первообразные, выполнить необходимые преобразования и получить ответ на заданный вопрос, учитывая формулу
Перед этим проверьте правильность моих предыдущих расчётов, потому что я не могу гарантировать их безошибочность.Можно, разумеется, поступить иначе. Для этого воспользуйтесь тем, что если
и -- частные решения соответственно уравненийи
то функция
является частным решением уравнения
Об авторе:
Facta loquuntur.
Facta loquuntur.
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