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Консультация № 186572
30.08.2012, 10:48
78.80 руб.
0
3
1
Здравствуйте! Прошу помощи в следующем вопросе:
решить дифференциальное уравнение
решить дифференциальное уравнение
Обсуждение
Неизвестный
30.08.2012, 12:05
общий
Только в распечатке примера как то не понятно написано или 
или 
. Посмотрите как правильнее.
или . Посмотрите как правильнее.
30.08.2012, 12:12
общий
Если спросить не у кого, сделайте скан примера. Загрузите файлик в мои файлы. Дайте ссылку. Посмотрим...
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
30.08.2012, 21:47
общий
это ответ
Здравствуйте, Посетитель - 375268!
Решается второй вариант:
4y2dx+(e1/(2y)+x)dy=0
dx/dy=-x/(4y2)-e1/(2y)/()(4y2)
Это линейное уравнение относительно x(y).
Решаем сначала однородное.
dx/dy=-x/(4y2)
dx/x=-dy/(4y2)
ln|x|=1/(4y)+const
x=Ce1/(4y)
Далее используем метод вариации: x=C(y)e1/(4y), получаем
C'(y)=-e1/(4y)/(4y2)=(e1/(4y))'
C(y)=e1/(4y)+C
Таким образом
x=e1/(2y)+Ce1/(4y)
Решается второй вариант:
4y2dx+(e1/(2y)+x)dy=0
dx/dy=-x/(4y2)-e1/(2y)/()(4y2)
Это линейное уравнение относительно x(y).
Решаем сначала однородное.
dx/dy=-x/(4y2)
dx/x=-dy/(4y2)
ln|x|=1/(4y)+const
x=Ce1/(4y)
Далее используем метод вариации: x=C(y)e1/(4y), получаем
C'(y)=-e1/(4y)/(4y2)=(e1/(4y))'
C(y)=e1/(4y)+C
Таким образом
x=e1/(2y)+Ce1/(4y)
Форма ответа
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