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Консультация № 192959
19.03.2018, 01:55
0.00 руб.
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
1) найти общее решение уравнения
y’=2xy/x^2-y^2
2)(xy’-y)arctg y/x=x;y|x=1 =0
3) (y^2-3x^2)dy+2xydx=0
4) y’+2y=4x
5) y’+y=cos x
6) y’=1/2x-y^2
1) найти общее решение уравнения
y’=2xy/x^2-y^2
2)(xy’-y)arctg y/x=x;y|x=1 =0
3) (y^2-3x^2)dy+2xydx=0
4) y’+2y=4x
5) y’+y=cos x
6) y’=1/2x-y^2
Обсуждение
19.03.2018, 08:19
общий
Адресаты:
Выберите любое из шести уравнений и сообщите, какие сложности у Вас возникли с его решением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
20.03.2018, 08:09
общий
Адресаты:
Зачем Вы не отвечаете на мой вопрос? Первому уравнению Вы решили посвятить отдельную консультацию, а с остальными разобрались, надо полагать?
Об авторе:
Facta loquuntur.
Facta loquuntur.
23.03.2018, 08:37
общий
это ответ
Здравствуйте, Elizabeth!
О том, как можно решить первое уравнение, я сообщил Вам в консультации, которую Вы посвятили этому уравнению. Аналогично можно решить и третье уравнение, потому что оно относится к тому же виду, что и первое.
Рассмотрим четвёртое уравнение. Оно имеет вид
где
-- постоянная, 
-- непрерывная функция. Значит, заданное уравнение является линейным уравнением первого порядка. Его можно решить как методом Бернулли (применив подстановку 
), так и методом Лагранжа (методом вариации произвольной постоянной). При использовании второго метода сначала нужно решить уравнение 
Получим 
Общее решение заданного уравнения будем искать в виде 
Тогда 
После подстановки в заданное уравнение получим 
Остаётся решить это уравнение относительно неизвестной функции 
и подставить в формулу 
чтобы выполнить задание.
Аналогично можно решить пятое уравнение.
О том, как можно решить первое уравнение, я сообщил Вам в консультации, которую Вы посвятили этому уравнению. Аналогично можно решить и третье уравнение, потому что оно относится к тому же виду, что и первое.
Рассмотрим четвёртое уравнение. Оно имеет вид
где
-- постоянная, -- непрерывная функция. Значит, заданное уравнение является линейным уравнением первого порядка. Его можно решить как методом Бернулли (применив подстановку ), так и методом Лагранжа (методом вариации произвольной постоянной). При использовании второго метода сначала нужно решить уравнение Получим Общее решение заданного уравнения будем искать в виде Тогда После подстановки в заданное уравнение получим Остаётся решить это уравнение относительно неизвестной функции и подставить в формулу чтобы выполнить задание.Аналогично можно решить пятое уравнение.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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