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Консультация № 203130
04.09.2022, 22:14
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе: Решить дифференциальное уравнение методом вариации произвольной постояной
Прикрепленные файлы:
Обсуждение
04.09.2022, 23:20
общий
это ответ
Это линейное неоднородное дифференциальное уравнение второго порядка с постоянными коэффициентами.
Соответствующее однородное уравнение:
Характеристическое уравнение:
Так как характеристическое уравнение имеет два сопряжённых чисто мнимых комплексных корня (
), то общее решение уравнения имеет вид 
Тогда для данного уравнения
Общее решение неоднородного уравнения будет искать в виде
Решим систему уравнений:
- правая часть исходного уравнения, 
- коэффициент перед 
в исходном уравнении
, значит, система имеет единственное решение
Общее решение уравнения:
Ответ:
, 
Прикрепленные файлы:
5
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