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Консультация № 194990
15.03.2019, 13:11
0.00 руб.
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите пожалуйста.Найти общий интеграл неоднородного дифференциального уравнения второго порядка:\
2y"+7y'+3y=222sin3x
Помогите пожалуйста.Найти общий интеграл неоднородного дифференциального уравнения второго порядка:\
2y"+7y'+3y=222sin3x
Обсуждение
15.03.2019, 13:50
общий
это ответ
Здравствуйте, Anna!
Это линейное неоднородное дифференциальное уравнение второго порядка с постоянными коэффициентами.
Соответствующее однородное уравнение:
Характеристическое уравнение соответствующего однородного уравнения имеет вид:
Найдем его корни:
Так как характеристическое уравнение имеет два различных действительных корня, то общее решение соответствующего однородного уравнения имеет вид
Тогда для данного уравнения
Так как характеристическое уравнение соответствующего однородного уравнения имеет два различных действительных корня,
то частное решение неоднородного уравнения будем искать в виде
Частное решение неоднородного уравнения:
Тогда общее решение данного уравнения:
Ответ:
Это линейное неоднородное дифференциальное уравнение второго порядка с постоянными коэффициентами.
Соответствующее однородное уравнение:
Характеристическое уравнение соответствующего однородного уравнения имеет вид:
Найдем его корни:
Так как характеристическое уравнение имеет два различных действительных корня, то общее решение соответствующего однородного уравнения имеет вид
Тогда для данного уравнения
Так как характеристическое уравнение соответствующего однородного уравнения имеет два различных действительных корня,
то частное решение неоднородного уравнения будем искать в виде
Частное решение неоднородного уравнения:
Тогда общее решение данного уравнения:
Ответ:
5
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