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Консультация № 194828
28.02.2019, 17:03
0.00 руб.
02.03.2019, 10:15
0
3
1
Здравствуйте! Прошу помощи в следующем вопросе:
Найти общее решение дифференциального уравнения и частное решение, удовлетворяющее начальному условию
Задание 4
Найти общее решение дифференциального уравнения и частное решение, удовлетворяющее начальному условию
Задание 4
Обсуждение
02.03.2019, 09:39
общий
это ответ
Здравствуйте, Aleksandrkib!
Имеем
-- линейное дифференциальное уравнение. Решим его методом И. Бернулли. Положим
Тогда 
Сначала решим уравнение
Теперь решим уравнение
Чтобы вычислить первообразную функцию (1), примем
Тогда 
Итак, общее решение заданного уравнения суть функция
Вычислим частное решение заданного уравнения. Получим
Значит, частное решение заданного уравнения, удовлетворяющее заданному начальному условию, суть функция
Имеем
-- линейное дифференциальное уравнение. Решим его методом И. Бернулли. Положим
Тогда Сначала решим уравнение
Теперь решим уравнение
Чтобы вычислить первообразную функцию (1), примем
Тогда Итак, общее решение заданного уравнения суть функция
Вычислим частное решение заданного уравнения. Получим
Значит, частное решение заданного уравнения, удовлетворяющее заданному начальному условию, суть функция
5
Спасибо за подробное решение!!!
Об авторе:
Facta loquuntur.
Facta loquuntur.
02.03.2019, 09:40
общий
Предлагаю дополнить сообщение, открывающее консультацию, текстом задания, который я набрал ниже.
Найти общее решение дифференциального уравнения и частное решение, удовлетворяющее начальному условию
Найти общее решение дифференциального уравнения и частное решение, удовлетворяющее начальному условию
Об авторе:
Facta loquuntur.
Facta loquuntur.
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