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Консультация № 194953
12.03.2019, 15:31
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Помогите пожалуйста с интегралами
Найти общий интеграл однородного дифференциального уравнения второго порядка:
а)y"-2y'+10y=0
б)y"+y'-2y=0
в)y"-2y'=0
Помогите пожалуйста с интегралами
Найти общий интеграл однородного дифференциального уравнения второго порядка:
а)y"-2y'+10y=0
б)y"+y'-2y=0
в)y"-2y'=0
Обсуждение
12.03.2019, 16:13
общий
это ответ
Здравствуйте, darina!
а)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
Так как характеристическое уравнение имеет два сопряженных комплексных корня
, то общее решение уравнения имеет вид 
Тогда общее решение данного уравнения
Ответ:
б)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
, 
Так как характеристическое уравнение имеет два различных действительных корня, то общее решение уравнения имеет вид
Тогда общее решение данного уравнения
Ответ:
в)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
, 
Так как характеристическое уравнение имеет два различных действительных корня, то общее решение уравнения имеет вид
Тогда общее решение данного уравнения
Ответ:
а)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
Так как характеристическое уравнение имеет два сопряженных комплексных корня
, то общее решение уравнения имеет вид Тогда общее решение данного уравнения
Ответ:
б)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
, Так как характеристическое уравнение имеет два различных действительных корня, то общее решение уравнения имеет вид
Тогда общее решение данного уравнения
Ответ:
в)
Это линейное однородное дифференциальное уравнение второго порядка с постоянными коэффициентами
Характеристическое уравнение имеет вид
Найдем его корни:
, Так как характеристическое уравнение имеет два различных действительных корня, то общее решение уравнения имеет вид
Тогда общее решение данного уравнения
Ответ:
5
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