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Консультация № 198002
20.03.2020, 09:51
0.00 руб.
0
3
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Как найти общее решение дифференциального уравнения первого порядка с разделяющимися переменными:
y sin xdx + cos x ln ydy = 0 ?
Как найти общее решение дифференциального уравнения первого порядка с разделяющимися переменными:
y sin xdx + cos x ln ydy = 0 ?
Обсуждение
20.03.2020, 11:31
общий
20.03.2020, 11:33
Адресаты:
Вам трудно решать потому что Вы не постарались аккуратно написать уравнение.
Преобразуем Вашу неряшливую запись в легко-осмысливаемую : y·sin(x)·dx = -cos(x)·ln(y)·dy
Разделяем переменные : Игреки влево, иксы вправо : [ln(y) / y]·dy = -[sin(x) / cos(x)]·dx
Интегрируем каждую часть равества отдельно: [$8747$][ln(y) / y]·dy = -[$8747$]tg(x)·dx
[ln(y)]2 / 2 = ln[cos(x)] + C1
см "Дифференциальные уравнения для чайников. Примеры решения" Ссылка1
Дальше сами справитесь?
Преобразуем Вашу неряшливую запись в легко-осмысливаемую : y·sin(x)·dx = -cos(x)·ln(y)·dy
Разделяем переменные : Игреки влево, иксы вправо : [ln(y) / y]·dy = -[sin(x) / cos(x)]·dx
Интегрируем каждую часть равества отдельно: [$8747$][ln(y) / y]·dy = -[$8747$]tg(x)·dx
[ln(y)]2 / 2 = ln[cos(x)] + C1
см "Дифференциальные уравнения для чайников. Примеры решения" Ссылка1
Дальше сами справитесь?
20.03.2020, 11:40
общий
Спасибо, Владимир Николаевич!
Дальше попробую сама! Ссылка как раз для меня))) именно чайник я и есть!
Дальше попробую сама! Ссылка как раз для меня))) именно чайник я и есть!
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