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Консультация № 190810
29.03.2017, 18:14
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Решить неоднородное диф-ое ур-е второго порядка с постоянными коэффициентами и специальной правой частью:
y``+3y`=9x
Решить неоднородное диф-ое ур-е второго порядка с постоянными коэффициентами и специальной правой частью:
y``+3y`=9x
Обсуждение
29.03.2017, 20:31
общий
это ответ
Здравствуйте, tolmachieva.a!
Правая часть заданного уравнения
имеет вид
где
Выведем общее решение дифференциального уравнения
Его характеристическое уравнение
имеет корни
Значит, общее решение уравнения
имеет вид
а частное решение уравнения
имеет вид
Тогда
Подставим выражения
в уравнение 
Получим
следовательно,
- общее решение заданного уравнения.
Правая часть заданного уравнения
имеет вид
где
Выведем общее решение дифференциального уравнения
Его характеристическое уравнение
имеет корни
Значит, общее решение уравнения
имеет вида частное решение уравнения
имеет видТогда
Подставим выражения
в уравнение Получимследовательно,
- общее решение заданного уравнения.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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