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Консультация № 186210
27.05.2012, 11:39
78.80 руб.
27.05.2012, 14:22
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
на фото: Задача N6; Вариант N14
фото:
на фото: Задача N6; Вариант N14
фото:
Обсуждение
27.05.2012, 12:46
общий
это ответ
Переходим к изображениям:
x''(t) -> p^2X(p)-px(0)-x'(0)=p^2X(p)-p
x'(t) -> pX(p)-x(0)=pX(p)-1
y''(t) -> p^2Y(p)-py(0)-y'(0)=p^2Y(p)-p
y'(t) -> pY(p)-y(0)=pY(p)-1
2 -> 2/p
cost -> p/(p^2+1)
p^2X(p)-p+X(p)+2pY(p)-2=2/p
p^2Y(p)-p+pX(p)-1=p/(p^2+1)
(p^2+1)X(p)+2pY(p)=p+2/p+2
pY(p)+X(p)=1/(p^2+1)+1+1/p
Решение системы:
X(p)=1/(p^2+1)+1/(p+1)
Y(p)=1/(p^2(1-p^2))-p/(1-p^2)=1/p^2+1/(p+1)
Возвращаемся к оригиналам:
x(t)=sint+1/e^t
y(t)=t+1/e^t
x''(t) -> p^2X(p)-px(0)-x'(0)=p^2X(p)-p
x'(t) -> pX(p)-x(0)=pX(p)-1
y''(t) -> p^2Y(p)-py(0)-y'(0)=p^2Y(p)-p
y'(t) -> pY(p)-y(0)=pY(p)-1
2 -> 2/p
cost -> p/(p^2+1)
p^2X(p)-p+X(p)+2pY(p)-2=2/p
p^2Y(p)-p+pX(p)-1=p/(p^2+1)
(p^2+1)X(p)+2pY(p)=p+2/p+2
pY(p)+X(p)=1/(p^2+1)+1+1/p
Решение системы:
X(p)=1/(p^2+1)+1/(p+1)
Y(p)=1/(p^2(1-p^2))-p/(1-p^2)=1/p^2+1/(p+1)
Возвращаемся к оригиналам:
x(t)=sint+1/e^t
y(t)=t+1/e^t
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