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Консультация № 183988
07.09.2011, 23:59
0.00 руб.
08.09.2011, 07:41
0
2
2
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
1) найти общее решение дифференциального уравнения первого порядка: XYштрих=x+y/2 и 2) найти общее решение линейного уравнения второго порядка Yдва штриха+Y=4SINX Спасибо!!!!!!!!!!
1) найти общее решение дифференциального уравнения первого порядка: XYштрих=x+y/2 и 2) найти общее решение линейного уравнения второго порядка Yдва штриха+Y=4SINX Спасибо!!!!!!!!!!
Обсуждение
08.09.2011, 04:59
общий
это ответ
Здравствуйте, леди!
Предлагаю решение 2 уравнения.
Будут вопросы обращайтесь в минифорум.
Удачи
Предлагаю решение 2 уравнения.
Будут вопросы обращайтесь в минифорум.
Удачи
08.09.2011, 07:04
общий
это ответ
Здравствуйте, леди!
1) Линейное уравнение. Пусть x[$8805$]0
Сначала решаем однородное
xy'=y/2
dy/y=dx/(2x)
ln|y|=(1/2)ln|x|+const
y=C[$8730$]x
Далее используем метод вариации:
y=C(x)[$8730$]x
Подставляя в уравнение, получаем
x[C'(x)[$8730$]x+C(x)/(2[$8730$]x)]=x+C[$8730$]x/2
C'(x)=1/[$8730$]x
C(x)=2[$8730$]x+C
Таким образом
y=2x+C[$8730$]x
При x<0 решение аналогично. Решение однородного y=C[$8730$](-x). Методом вариации получаем уравнение
C'(x)=1/[$8730$](-x)
C(x)=-2[$8730$](-x)+C
y=2x+C[$8730$](-x)
Оба случая легко объединить в один
y=2x+C[$8730$]|x|
1) Линейное уравнение. Пусть x[$8805$]0
Сначала решаем однородное
xy'=y/2
dy/y=dx/(2x)
ln|y|=(1/2)ln|x|+const
y=C[$8730$]x
Далее используем метод вариации:
y=C(x)[$8730$]x
Подставляя в уравнение, получаем
x[C'(x)[$8730$]x+C(x)/(2[$8730$]x)]=x+C[$8730$]x/2
C'(x)=1/[$8730$]x
C(x)=2[$8730$]x+C
Таким образом
y=2x+C[$8730$]x
При x<0 решение аналогично. Решение однородного y=C[$8730$](-x). Методом вариации получаем уравнение
C'(x)=1/[$8730$](-x)
C(x)=-2[$8730$](-x)+C
y=2x+C[$8730$](-x)
Оба случая легко объединить в один
y=2x+C[$8730$]|x|
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