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Консультация № 55201
12.09.2006, 20:43
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Плззз помогите решить...http://slil.ru/23114344
P.S. Sorry что напечатать не смог =\ не получалось =\
P.S. Sorry что напечатать не смог =\ не получалось =\
Обсуждение
Неизвестный
13.09.2006, 12:52
общий
это ответ
Здравствуйте, Kill_me_baby!
Очень странное условие на собственное значение, ведь и без этого условия можно найти все собственные значения из уравнения det|A-λE|=0, и, действительно
-λ^3+14λ^2+112λ+160=0; λ1=-2, λ2=-4, λ3=20
т.о. решение ищется в виде
X=C1*e^(-2t)+C2*e^(-4t)+C3*e^(20t), где C1,C2,C3 произвольные векторные константы, которые должны сводится только к трём произвольным константам,
подставив искомое выражение в исходную систему X‘=AX
X‘=-2C1*e^(-2t)+-4C2*e^(-4t)+20C3*e^(20t)=A*C1*e^(-2t)+A*C2*e^(-4t)+A*C3*e^(20t)
а уж потом, эти три произвольные константы находятся из задачи Коши X(0)=(3,5,8)
Удачи!
Очень странное условие на собственное значение, ведь и без этого условия можно найти все собственные значения из уравнения det|A-λE|=0, и, действительно
-λ^3+14λ^2+112λ+160=0; λ1=-2, λ2=-4, λ3=20
т.о. решение ищется в виде
X=C1*e^(-2t)+C2*e^(-4t)+C3*e^(20t), где C1,C2,C3 произвольные векторные константы, которые должны сводится только к трём произвольным константам,
подставив искомое выражение в исходную систему X‘=AX
X‘=-2C1*e^(-2t)+-4C2*e^(-4t)+20C3*e^(20t)=A*C1*e^(-2t)+A*C2*e^(-4t)+A*C3*e^(20t)
а уж потом, эти три произвольные константы находятся из задачи Коши X(0)=(3,5,8)
Удачи!
Неизвестный
13.09.2006, 12:55
общий
Т.к. по условию уже дано одно собственное значение, возможно, что как раз и имелось в виду отыскание решения отвечающего этому собственному значениют.е. X=Ce^(-2t)но, тогда задача Коши сводится к тому, что X(0)=(c1,c2,c3)=(3,5,8)т.о. решение будет иметь видX=(3,5,8)*e^(-2t)
Неизвестный
13.09.2006, 21:20
общий
Спасибо!P.S. Если честно, то это нам дали на выполнение в инсте! МГИЭМ!
Неизвестный
13.09.2006, 21:26
общий
А можно ещё спросить?? Ммм што значит уравнениеdet|A-λE|=0 ?? "det"?
Неизвестный
14.09.2006, 00:24
общий
Вы если уж не печатаете текст задания, то хотя бы пишите, по какой тематике.
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