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Консультация № 187720
26.01.2014, 19:48
180.00 руб.
0
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1
Обсуждение
26.01.2014, 21:49
общий
это ответ
Здравствуйте, Барс Иван!
Решение системы 1.
Task0.doc (239.5 кб)
Решение системы 2.
Заменой u=v+(3t2/2) освобождаемся от неоднородности в уравнении, получаем задачу
vt=vxx
v(x,0)=sin x
Решение этой задачи можно искать в виде v(x)=T(t)sin x
Начальное условие равносильно T(0)=1
Так как vt=T'(t)sin x, vxx=-T(t)sin x, то уравнение равносильно T'(t)=-T(t)
Решая теперь задачу Коши для обыкновенного дифференциального уравнения
T'(t)=-T(t)
T(0)=1
находим T(t)=e-t
Ответ:
u(x,t)=e-tsin x+(3t2/2)
Решение системы 1.
Task0.doc (239.5 кб)
Решение системы 2.
Заменой u=v+(3t2/2) освобождаемся от неоднородности в уравнении, получаем задачу
vt=vxx
v(x,0)=sin x
Решение этой задачи можно искать в виде v(x)=T(t)sin x
Начальное условие равносильно T(0)=1
Так как vt=T'(t)sin x, vxx=-T(t)sin x, то уравнение равносильно T'(t)=-T(t)
Решая теперь задачу Коши для обыкновенного дифференциального уравнения
T'(t)=-T(t)
T(0)=1
находим T(t)=e-t
Ответ:
u(x,t)=e-tsin x+(3t2/2)
26.01.2014, 23:03
общий
26.01.2014, 23:06
Адресаты:
Дмитрий Германович!
Замените, пожалуйста, ссылку на решение системы 1 на следующую:
.
Если решение не будет отображаться, то это связано с проблемами на сервере. Дайте автору вопроса ссылку на решение, размещённое на стороннем ресурсе, или отправьте на указанный им адрес по договорённости.
Замените, пожалуйста, ссылку на решение системы 1 на следующую:
Если решение не будет отображаться, то это связано с проблемами на сервере. Дайте автору вопроса ссылку на решение, размещённое на стороннем ресурсе, или отправьте на указанный им адрес по договорённости.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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