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Консультация № 197436
15.12.2019, 05:16
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Здравствуйте! Прошу помощи в решении этого дифференциального уравнения: ysinx+y'cosx=1
Обсуждение
20.12.2019, 02:30
общий
это ответ
Здравствуйте, PavelKotik!
Запишем уравнение в виде
Это уравнение Бернулли, которое решается путём замены y = uv, y' = u'v + uv'. В данном случае получится
Получаем два уравнения с разделяющимися переменными:
и
В качестве v(x) выберем частное решение первого уравнения:
Подставим это решение во второе уравнение:
Тогда общим решением будет
Запишем уравнение в виде
Это уравнение Бернулли, которое решается путём замены y = uv, y' = u'v + uv'. В данном случае получится
Получаем два уравнения с разделяющимися переменными:
и
В качестве v(x) выберем частное решение первого уравнения:
Подставим это решение во второе уравнение:
Тогда общим решением будет
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