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Консультация № 199923
20.12.2020, 12:06
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Определить тип и решить дифференциальное уравнение:
y^'=2xy+x
Определить тип и решить дифференциальное уравнение:
y^'=2xy+x
Прикрепленные файлы:
Обсуждение
24.12.2020, 17:19
общий
это ответ
Здравствуйте, Barsik22!
Уравнение вида
где функции P(x), Q(x) известны, называется линейным уравнением первого порядка. Оно решается путём замены y(x) = u(x)v(x), преобразующей его к виду
или
Выбираем функцию v(x) так, чтобы выполнялось условие
Решая это однородное уравнение, получаем
Тогда функция u(x) будет решением уравнения
то есть
В данном случае
уравнение
можно записать в виде
тогда P(x) = -2x, Q(x) = x и решением уравнениея
будет функция
а решением уравнения
- функция
Тогда
- общее решение исходного уравнения.
Уравнение вида
где функции P(x), Q(x) известны, называется линейным уравнением первого порядка. Оно решается путём замены y(x) = u(x)v(x), преобразующей его к виду
или
Выбираем функцию v(x) так, чтобы выполнялось условие
Решая это однородное уравнение, получаем
Тогда функция u(x) будет решением уравнения
то есть
В данном случае
уравнение
можно записать в виде
тогда P(x) = -2x, Q(x) = x и решением уравнениея
будет функция
а решением уравнения
- функция
Тогда
- общее решение исходного уравнения.
5
Спасли меня!
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