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Консультация № 188639
14.01.2016, 11:06
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Здравствуйте! У меня возникли сложности с таким вопросом: Найти общее решение дифференциального уравнения второго порядка: y'' - 2y' = ex(x2+x-3)/ Сформулировать задачу Коши для этого уравнения, задав корректные начальные условия для искомой функции.
Общее решение я нашла: y = C1 + C2e2x+(-x2-x+1)ex, Проблема сформулировать задачу Коши.
Общее решение я нашла: y = C1 + C2e2x+(-x2-x+1)ex, Проблема сформулировать задачу Коши.
Обсуждение
14.01.2016, 12:00
общий
это ответ
Здравствуйте, bolrunoff-kati!
Задача Коши для дифференциального уравнения второго порядка записывается в общем виде следующим образом:
Согласно известной теореме, условием существования и единственности решения задачи Коши является непрерывность функции
и её частных производных 
в некоторой области 
изменения переменных 
Если общее решение дифференциального уравнения второго порядка имеет вид
(проверять не буду), то
Условие теоремы в данном случае выполняется.
Положим, например,
Пусть 
Тогда
Значит, задача Коши в данном случае записывается так:
Разумеется, это не единственная возможность.
С уважением.
Задача Коши для дифференциального уравнения второго порядка записывается в общем виде следующим образом:
Согласно известной теореме, условием существования и единственности решения задачи Коши является непрерывность функции
и её частных производных в некоторой области изменения переменных Если общее решение дифференциального уравнения второго порядка имеет вид
(проверять не буду), то
Условие теоремы в данном случае выполняется.
Положим, например,
Пусть ТогдаЗначит, задача Коши в данном случае записывается так:
Разумеется, это не единственная возможность.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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