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Консультация № 186209
27.05.2012, 11:35
78.80 руб.
27.05.2012, 14:23
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
на фото: Задача N5; Вариант N7;
фото:
на фото: Задача N5; Вариант N7;
фото:
Обсуждение
27.05.2012, 20:00
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'
e^t -> 1/(p-1)
p^2x(p)-pX0-X0'-4px(p)+4X0+5x(p)=1/(p-1)
x(p)(p^2-4p+5)=1/(p-1)+(p-4)X0+X0'
x(p)=1/((p-1)((p-2)^2+1))+(p-4)X0/((p-2)^2+1)+X0'/((p-2)^2+1)=1/(2(p-1))-(p-2)/(2((p-2)^2+1))+1/(2((p-2)^2+1))+(p-2)X0/((p-2)^2+1)+(X0'-2X0)/((p-2)^2+1)
Возвращаемся к оригиналам:
X(t)=(e^t)/2+(X0-1/2)*e^(2t)*cost+(X0'-2X0+1/2)*e^(2t)*sint
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'
e^t -> 1/(p-1)
p^2x(p)-pX0-X0'-4px(p)+4X0+5x(p)=1/(p-1)
x(p)(p^2-4p+5)=1/(p-1)+(p-4)X0+X0'
x(p)=1/((p-1)((p-2)^2+1))+(p-4)X0/((p-2)^2+1)+X0'/((p-2)^2+1)=1/(2(p-1))-(p-2)/(2((p-2)^2+1))+1/(2((p-2)^2+1))+(p-2)X0/((p-2)^2+1)+(X0'-2X0)/((p-2)^2+1)
Возвращаемся к оригиналам:
X(t)=(e^t)/2+(X0-1/2)*e^(2t)*cost+(X0'-2X0+1/2)*e^(2t)*sint
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