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Консультация № 184096

26.09.2011, 20:57

51.74 руб.

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Образование

Здравствуйте! У меня возникли сложности с таким вопросом: решить операторным методом дифференциальное уравнение x"-x'=1, x(0)=-1, x'(0)=-1 Срочно надо!!!

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

26.09.2011, 22:46

общий

это ответ

Здравствуйте, Ольга Никанова!
Пусть X(t)[$8594$]F(p). Согласно свойствам преобразования Лапласа
X'(t)[$8594$]pF(p)-X(0)=pF(p)+1
X''(t)[$8594$]p²F(p)-pX(0)-X'(0)=p²F(p)+p+1
1[$8594$]1/p
В образах Лапласа получаем уравнение
(p²F(p)+p+1)-(pF(p)+1)=1/p
Решая уравнение, находим
F(p)=-(1/p²)-1/p
Беря обратное преобразование Лапласа (по таблице), получаем
X(t)=-t-1

Неизвестный

26.09.2011, 23:40

общий

Адресаты:

https://rfpro.ru/question/184097 Помогите,пожалуйста,с этим вопросом до утра надо решить! Я отблагодарю

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