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Консультация № 195495
03.05.2019, 19:48
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти решение дифференциального уравнения
y'' + 4y' - 12y =81 exp(3x)
Найти решение дифференциального уравнения
y'' + 4y' - 12y =81 exp(3x)
Обсуждение
05.05.2019, 08:41
общий
это ответ
Здравствуйте, mustang289!
Решим сначала уравнение
с нулевой правой частью. Его характеристическое уравнение 
имеет действительные корни 
Поэтому общее решение уравнения с нулевой частью -- функция 
Правая часть заданного уравнения имеет вид
где 
Число 
не является корнем характеристического уравнения, рассмотренного выше. Значит, частное решение заданного уравнения имеет вид 
Тогда 
-- частное решение заданного уравнения.
Следовательно, общее решение заданного уравнения суть функция
Решим сначала уравнение
с нулевой правой частью. Его характеристическое уравнение имеет действительные корни Поэтому общее решение уравнения с нулевой частью -- функция Правая часть заданного уравнения имеет вид
где Число не является корнем характеристического уравнения, рассмотренного выше. Значит, частное решение заданного уравнения имеет вид Тогда -- частное решение заданного уравнения.Следовательно, общее решение заданного уравнения суть функция
Об авторе:
Facta loquuntur.
Facta loquuntur.
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