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Консультация № 189746
06.09.2016, 15:00
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
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Обсуждение
07.09.2016, 07:57
общий
это ответ
Здравствуйте, line-di!
Решение второго уравнениея.
Перепишем уравнение в виде
y' = (2 - y)/ctg(x) = (2-y)*tg(x),
y'/(y-2) = -tg(x),
d(y-2)/(y-2) = -tg(x)dx = -sin(x)dx/cos(x) = d(cos(x))/cos(x).
Интегрируем:
ln|y-2|=ln|cos(x)|+ln|C|, откуда находим общее решение
у-2 = С*cos(x).
Подставляя x=0,y=2, получим C=0, т.е., решение, удовлетворяющее начальным условиям, будет
y(x) = 2 при всех значениях x.
Проверкой убеждаемся, что это решение удовлетворяет уравнению и начальным условиям.
Решение второго уравнениея.
Перепишем уравнение в виде
y' = (2 - y)/ctg(x) = (2-y)*tg(x),
y'/(y-2) = -tg(x),
d(y-2)/(y-2) = -tg(x)dx = -sin(x)dx/cos(x) = d(cos(x))/cos(x).
Интегрируем:
ln|y-2|=ln|cos(x)|+ln|C|, откуда находим общее решение
у-2 = С*cos(x).
Подставляя x=0,y=2, получим C=0, т.е., решение, удовлетворяющее начальным условиям, будет
y(x) = 2 при всех значениях x.
Проверкой убеждаемся, что это решение удовлетворяет уравнению и начальным условиям.
постольку
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