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Консультация № 194829
28.02.2019, 17:08
0.00 руб.
03.03.2019, 10:07
0
4
1
Здравствуйте! У меня возникли сложности с таким вопросом:
https://rfpro.ru/upload/11435 - Задание 5
Найти решение дифференциального уравнения
P.S. Заранее извините за вопрос, давным-давно здесь не был. Раньше, когда отправляли вопрос, оценивали его стоимость. Теперь не совсем понял, как заплатить эксперту за решение, если таковое будет представлено. Не бесплатно же они будут решать задачи.
https://rfpro.ru/upload/11435 - Задание 5
Найти решение дифференциального уравнения
P.S. Заранее извините за вопрос, давным-давно здесь не был. Раньше, когда отправляли вопрос, оценивали его стоимость. Теперь не совсем понял, как заплатить эксперту за решение, если таковое будет представлено. Не бесплатно же они будут решать задачи.
Обсуждение
28.02.2019, 17:39
общий
Адресаты:
На радость Вам, у нас теперь всё бесплатно, но и гарантий никаких. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
03.03.2019, 08:41
общий
это ответ
Здравствуйте, Aleksandrkib!
Решим сначала соответствующее уравнение с нулевой правой частью
Корнями его характеристического уравнения
являются комплексные числа
Поэтому общее решение уравнения (1) суть функция
Правая часть
заданного дифференциального уравнения является квадратным трёхчленом; поэтому частное решение заданного уравнения можно вычислить методом неопределённых коэффициентов. Запишем 
Поскольку 
не является корнем характеристического уравнения (2), постольку частное решение заданного уравнения имеет вид 
При этом 
Подставив 
в заданное уравнение, получим
Приравнивая коэффициенты при одинаковых степенях
в левой и правой частях последнего уравнения, получим, что 
Значит,
-- частное решение заданного уравнения,
-- общее решение заданного уравнения.
Решим сначала соответствующее уравнение с нулевой правой частью
Корнями его характеристического уравнения
являются комплексные числа
Поэтому общее решение уравнения (1) суть функцияПравая часть
заданного дифференциального уравнения является квадратным трёхчленом; поэтому частное решение заданного уравнения можно вычислить методом неопределённых коэффициентов. Запишем Поскольку не является корнем характеристического уравнения (2), постольку частное решение заданного уравнения имеет вид При этом Подставив в заданное уравнение, получимПриравнивая коэффициенты при одинаковых степенях
в левой и правой частях последнего уравнения, получим, что Значит, -- частное решение заданного уравнения, -- общее решение заданного уравнения.
5
Спасибо за подробное решение!!!
Об авторе:
Facta loquuntur.
Facta loquuntur.
03.03.2019, 08:42
общий
Предлагаю дополнить сообщение, открывающее консультацию, текстом задания, который я набрал ниже.
Найти решение дифференциального уравнения
Найти решение дифференциального уравнения
Об авторе:
Facta loquuntur.
Facta loquuntur.
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