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Консультация № 203136
05.09.2022, 14:43
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Даны дифференциальные уравнения второго порядка. Найти общее решение этих уравнений.
Даны дифференциальные уравнения второго порядка. Найти общее решение этих уравнений.
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Обсуждение
06.09.2022, 06:32
общий
это ответ
Здравствуйте, Anna!
Рассмотрим линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Его характеристическое уравнение суть 
Решая это уравнение, получим, что 
То есть однократными корнями характеристического уравнения являются вещественные числа 
и 
Значит, общее решение заданного дифференциального уравнения имеет вид
Рассмотрим линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Его характеристическое уравнение суть Решая это уравнение, получим, что То есть однократными корнями характеристического уравнения являются вещественные числа и Значит, общее решение заданного дифференциального уравнения имеет вид
Об авторе:
Facta loquuntur.
Facta loquuntur.
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