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Консультация № 198819
01.06.2020, 20:36
0.00 руб.
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Определить тип и решить дифференциальное уравнение:
(у+sqrt(xy))dx=xdy
Определить тип и решить дифференциальное уравнение:
(у+sqrt(xy))dx=xdy
Прикрепленные файлы:
Обсуждение
06.06.2020, 19:01
общий
это ответ
Здравствуйте, Людмила!
Разделив обе части уравнения на x dx, получаем
Уравнения вида y' = f(y/x), в которых производная является функцией не переменных x и y, а только их отношения y/x, называются однородными уравнениями первого порядка и решаются путём замены y = ux, dy = x du + u dx. В данном случае исходное уравнение
после такой замены примет вид
откуда путём обратной замены u = y/x получаем
Разделив обе части уравнения на x dx, получаем
Уравнения вида y' = f(y/x), в которых производная является функцией не переменных x и y, а только их отношения y/x, называются однородными уравнениями первого порядка и решаются путём замены y = ux, dy = x du + u dx. В данном случае исходное уравнение
после такой замены примет вид
откуда путём обратной замены u = y/x получаем
5
Большое спасибо!
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