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Консультация № 188205
16.11.2015, 22:03
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Нужно решить систему ДУ операторным методом
x'+4x+4y=0
y'+2x+6y=0
x(0)=3
y(0)=15
Нужно решить систему ДУ операторным методом
x'+4x+4y=0
y'+2x+6y=0
x(0)=3
y(0)=15
Обсуждение
17.11.2015, 04:13
общий
это ответ
Здравствуйте, Василенко Иван Владимирович !
По таблице для преобразования Лапласа:
В данном случае
или после подстановки и упрощения:
Из первого уравнения
Подставляя во второе уравнение, получаем
или
откуда
Воспользовавшись преобразованием Лапласа:
получаем оригиналы
и решением системы будет
По таблице для преобразования Лапласа:
В данном случае
или после подстановки и упрощения:
Из первого уравнения
Подставляя во второе уравнение, получаем
или
откуда
Воспользовавшись преобразованием Лапласа:
получаем оригиналы
и решением системы будет
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