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Консультация № 181340
14.12.2010, 04:04
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Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Проверить, удовлетворяет ли заданному уравнению функция u=u(x,y).
X^2 (d^2 u/dx )+ y^2 (d^2u/dy^2)=0, Если u=е^(xy) .
Проверить, удовлетворяет ли заданному уравнению функция u=u(x,y).
X^2 (d^2 u/dx )+ y^2 (d^2u/dy^2)=0, Если u=е^(xy) .
Обсуждение
14.12.2010, 04:38
общий
это ответ
Здравствуйте, Клещенок Инна Владимировна!
Если я правильно понял условие, то имеем функцию двух переменных и в дифференциальном уравнении речь идет о частных производных. Найдем соответствующие частные производные:
du/dx=exy*y
d2u/dx2=exy*y*y=exy*y2 (находим частную производную по х, в этом случае у считаем константой)
du/dy=exy*x
d2u/dy2=exy*x*x=exy*x2 (находим частную производную по y, в этом случае x считаем константой)
Подставляем найденные значения в дифференциальное уравнением, получаем:
x2*y2*exy+x2*y2*exy=0
2*x2*y2*exy=0
Если уравнение записано верно, то делаем вывод о том, что заданному уравнению данная функция не удовлетворяет.
P.S. Если все же в уравнении будет знак минус, то функция будет удовлетворять.
Будут вопросы обращайтесь в минифорум.
Удачи
Если я правильно понял условие, то имеем функцию двух переменных и в дифференциальном уравнении речь идет о частных производных. Найдем соответствующие частные производные:
du/dx=exy*y
d2u/dx2=exy*y*y=exy*y2 (находим частную производную по х, в этом случае у считаем константой)
du/dy=exy*x
d2u/dy2=exy*x*x=exy*x2 (находим частную производную по y, в этом случае x считаем константой)
Подставляем найденные значения в дифференциальное уравнением, получаем:
x2*y2*exy+x2*y2*exy=0
2*x2*y2*exy=0
Если уравнение записано верно, то делаем вывод о том, что заданному уравнению данная функция не удовлетворяет.
P.S. Если все же в уравнении будет знак минус, то функция будет удовлетворять.
Будут вопросы обращайтесь в минифорум.
Удачи
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