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Консультация № 189873
11.10.2016, 18:42
0.00 руб.
0
2
1
Уважаемые эксперты! Пожалуйста, помогите решить дифференциальное уравнение:
Приложение:
(y/x^2)dx-((xy+1)/x)dy=0
Приложение:
(y/x^2)dx-((xy+1)/x)dy=0
Обсуждение
11.10.2016, 20:18
общий
это ответ
Здравствуйте, user8351!
Пусть дано дифференциальное уравнение
Попробуем подобрать такое число
чтобы левая часть этого уравнения стала однородной функцией некоторой степени 
относительно 
при условии, что 
считается величиной первого измерения, 
- 
-го измерения, а 
и 
- величинами соответственно нулевого и 
-го измерений. При этом 
- величина -го измерения. При этом предположении члены левой части являются величинами следующих измерений:
-
измерения 
-
измерения 
-
измерения 
Решая уравнение
получим 
Значит, уравнение 
можно рассматривать как обобщённое однородное уравнение и свести к уравнению с разделяющимися переменными при помощи подстановки
где
- новая неизвестная функция.
Из формулы
и уравнения получим
Выражение
является общим интегралом уравнения 
За безошибочность предложенного решения не ручаюсь. Поэтому Вам предстоит внимательно проверить его.
Пусть дано дифференциальное уравнение
Попробуем подобрать такое число
чтобы левая часть этого уравнения стала однородной функцией некоторой степени относительно при условии, что считается величиной первого измерения, - -го измерения, а и - величинами соответственно нулевого и -го измерений. При этом - величина -го измерения. При этом предположении члены левой части являются величинами следующих измерений:-
измерения -
измерения -
измерения Решая уравнение
получим Значит, уравнение можно рассматривать как обобщённое однородное уравнение и свести к уравнению с разделяющимися переменными при помощи подстановкигде
- новая неизвестная функция.Из формулы
и уравнения получимВыражение
является общим интегралом уравнения За безошибочность предложенного решения не ручаюсь. Поэтому Вам предстоит внимательно проверить его.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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