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Консультация № 183215
17.05.2011, 18:40
50.05 руб.
19.05.2011, 10:03
0
14
4
Здравствуйте! Прошу помощи в следующем вопросе: https://rfpro.ru/upload/5575/ Хотя бы начало решения каждого примера,подскажите,пожалуйста.
m=4 и n=3
m=4 и n=3
Обсуждение
17.05.2011, 19:49
общий
Мне кажется, что значения m и n дожны быть конкретизированы в зависимости от варианта. Иначе становится долгим исследование параметров.
Неизвестный
17.05.2011, 19:55
общий
это ответ
Здравствуйте, Ольга Никанова!
а) Сделаем замену переменной e[sup]ny[/sup]=z(x). Отсюда y=(ln z)/n -> y'=z'/(nz).
Подставим в уравнение, получим
Теперь получим
Ответ:
[editformula]
а) Сделаем замену переменной e[sup]ny[/sup]=z(x). Отсюда y=(ln z)/n -> y'=z'/(nz).
Подставим в уравнение, получим
Теперь получим
Ответ:
[editformula]
17.05.2011, 19:55
общий
это ответ
Здравствуйте, Ольга Никанова!
б) y'=(mx+ny)/(nx-my)=(m+n(y/x))/(n-m(y/x))
Делаем замену z=y/x; y=zx, получаем
z'x+z=(m+nz)/(n-mz)
z'x=m(1+z2)/n-mz
(n-mz)dz/(1+z2)=mdx/x
n*arctg z-(m/2)ln(1+z2)=m*ln|x|+C
n*arctg(y/x)-(m/2)ln(1+(y2x2/)=m*ln|x|+C
б) y'=(mx+ny)/(nx-my)=(m+n(y/x))/(n-m(y/x))
Делаем замену z=y/x; y=zx, получаем
z'x+z=(m+nz)/(n-mz)
z'x=m(1+z2)/n-mz
(n-mz)dz/(1+z2)=mdx/x
n*arctg z-(m/2)ln(1+z2)=m*ln|x|+C
n*arctg(y/x)-(m/2)ln(1+(y2x2/)=m*ln|x|+C
18.05.2011, 05:22
общий
это ответ
Здравствуйте, Ольга Никанова!
в)
г)
Лучше все перепроверить. Будут вопросы обращайтесь в минифорум.
Удачи
в)
г)
Лучше все перепроверить. Будут вопросы обращайтесь в минифорум.
Удачи
Неизвестный
18.05.2011, 23:47
общий
Спасибо. Помогите,пожалуйста с примером (в).Там, как я понимаю надо разделить обе части на (16+x^2), потом замена у=uv и т.д. Только я совсем запуталась в дифференцировании в решении.Ничего не выходит(((
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