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Консультация № 160285
12.02.2009, 12:41
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Добрый день! Подскажите пожалуйста,
надо решить задание, ничего не получается:
найти общее решение дифференциального уравнение и построить графики двух различных частных решений этого уравнения: y`=1+y^2
надо решить задание, ничего не получается:
найти общее решение дифференциального уравнение и построить графики двух различных частных решений этого уравнения: y`=1+y^2
Обсуждение
Неизвестный
12.02.2009, 13:08
общий
это ответ
Здравствуйте, Валерия Владимировна!
y' = dy/dx .
dy/dx = 1+y^2
Решаем уравнение с разделяющимися переменными
dy/(1+y^2) = dx
Интегрируем и получаем:
arctgy = x+C
отсюда y = tg(x+C)
Это общее решение. Для ответа на второй вопрос можно построить например,
графики y=tgx и y=tg(x+1)
y' = dy/dx .
dy/dx = 1+y^2
Решаем уравнение с разделяющимися переменными
dy/(1+y^2) = dx
Интегрируем и получаем:
arctgy = x+C
отсюда y = tg(x+C)
Это общее решение. Для ответа на второй вопрос можно построить например,
графики y=tgx и y=tg(x+1)
Форма ответа
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