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Консультация № 186208
27.05.2012, 11:32
78.80 руб.
27.05.2012, 14:25
0
3
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
на фото: Задача N5; Вариант N14;
фото:
на фото: Задача N5; Вариант N14;
фото:
Обсуждение
27.05.2012, 19:26
общий
это ответ
Здравствуйте, Artek9300!
Переходим к изображениям:
X(t) -> x(p)
X'(t) -> px(p)-X(0)=px(p)-X0
X''(t) -> p^2x(p)-pX(0)-X'(0)=p^2x(p)-pX0-X0'
t -> 1/p^2
p^2x(p)-pX0-X0'-px(p)+X0-2x(p)=1/p^2
x(p)(p^2-p-2)=1/p^2+(p-1)X0+X0'
x(p)=-1/(2p^2)+1/(4p)-1/(3(p+1))+1/(12(p-2))+2X0/(3(p+1))+X0/(3(p-2))-X0'/(3(p+1))+X0'/(3(p-2))
Возвращаемся к оригиналам:
X(t)=-t/2+1/4+(2X0-1-X0')/(3e^t)+(4X0+1+4X0')(e^(2t))/12
Переходим к изображениям:
X(t) -> x(p)
X'(t) -> px(p)-X(0)=px(p)-X0
X''(t) -> p^2x(p)-pX(0)-X'(0)=p^2x(p)-pX0-X0'
t -> 1/p^2
p^2x(p)-pX0-X0'-px(p)+X0-2x(p)=1/p^2
x(p)(p^2-p-2)=1/p^2+(p-1)X0+X0'
x(p)=-1/(2p^2)+1/(4p)-1/(3(p+1))+1/(12(p-2))+2X0/(3(p+1))+X0/(3(p-2))-X0'/(3(p+1))+X0'/(3(p-2))
Возвращаемся к оригиналам:
X(t)=-t/2+1/4+(2X0-1-X0')/(3e^t)+(4X0+1+4X0')(e^(2t))/12
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