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Консультация № 195319
20.04.2019, 16:46
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Решить уравнение методом вариации произвольных постоянных:
Решить уравнение методом вариации произвольных постоянных:
Прикрепленные файлы:
Обсуждение
22.04.2019, 11:34
общий
это ответ
Здравствуйте, Лилия!
Определим общее решение
соответствующего уравнения с правой частью, равной нулю, то есть 
Решая характеристическое уравнение, получим 
Значит, 
Определим частное решение
заданного уравнения в виде 
Чтобы вычислить 
и 
составим систему уравнений
соответствующую формуле (5.9) [1, с. 41]. Решая эту систему уравнений, получим
Тогда
Следовательно, общее решение заданного уравнения имеет вид
Полученное выражение можно преобразовать дальше, но я не вижу необходимости в этом.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 2. -- М.: Айрис-пресс, 2006. -- 256 с.
Определим общее решение
соответствующего уравнения с правой частью, равной нулю, то есть Решая характеристическое уравнение, получим Значит, Определим частное решение
заданного уравнения в виде Чтобы вычислить и составим систему уравненийсоответствующую формуле (5.9) [1, с. 41]. Решая эту систему уравнений, получим
Тогда
Следовательно, общее решение заданного уравнения имеет вид
Полученное выражение можно преобразовать дальше, но я не вижу необходимости в этом.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 2. -- М.: Айрис-пресс, 2006. -- 256 с.
5
Спасибо
Об авторе:
Facta loquuntur.
Facta loquuntur.
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