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Консультация № 197376
11.12.2019, 18:17
0.00 руб.
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Здравствуйте, помогите решить данное дифференциальное уравнение.
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Обсуждение
16.12.2019, 18:25
общий
это ответ
Здравствуйте, garwin!
Это уравнение Бернулли. 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
С учётом начального условия
имеем C = 0 и
Это уравнение Бернулли. 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
С учётом начального условия
имеем C = 0 и
5
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