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Консультация № 197374
11.12.2019, 16:51
0.00 руб.
15.12.2019, 09:07
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите решить задачу!
Помогите решить задачу!
Обсуждение
15.12.2019, 10:25
общий
это ответ
Здравствуйте, nata!
Разделив обе части уравнения на x dx, получим
или
Дифференциальные уравнение подобного вида, где производная зависит только от отношения y/x[sup]n[/sup], называются однородными уравнениями n-го порядка и решаются путём замены y(x) = x[sup]n[/sup]u(x). В данном случае имеем однородное уравнение первого порядка, которое путём замены y = xu, y' = u + xu' приводится к виду
откуда
Интегрируя, получаем
откуда, с учётом обратной замены u = y/x,
Разделив обе части уравнения на x dx, получим
или
Дифференциальные уравнение подобного вида, где производная зависит только от отношения y/x[sup]n[/sup], называются однородными уравнениями n-го порядка и решаются путём замены y(x) = x[sup]n[/sup]u(x). В данном случае имеем однородное уравнение первого порядка, которое путём замены y = xu, y' = u + xu' приводится к виду
откуда
Интегрируя, получаем
откуда, с учётом обратной замены u = y/x,
5
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