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Консультация № 193402
18.06.2018, 13:24
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти общее решение уравнения y''-14y'+53y=53x^3-42x^2+59x-14
Найти общее решение уравнения y''-14y'+53y=53x^3-42x^2+59x-14
Обсуждение
19.06.2018, 06:44
общий
Адресаты:
Какие сложности с этим вопросом у Вас возникли?
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.06.2018, 09:23
общий
это ответ
Здравствуйте, Tata1207!
Вам дано линейное неоднородное уравнение второго порядка с постоянными коэффициентами. Общее решение этого уравнения равно сумме общего решения соответствующего однородного уравнения и какого-либо частного решения заданного неоднородного уравнения.
Вычислим сначала общее решение соответствующего однородного уравнения, то есть уравнения
Составим характеристическое уравнение
и, решая его, вычислим корни: 
Значит, общее решение уравнения 
-- функция
Чтобы вычислить частное решение заданного дифференциального уравнения, можно воспользоваться тем, что его правая часть
является многочленом третьей степени. Я предлагаю Вам прочитать эту статью, внимательно разобрать примеры и вычислить частное решение самостоятельно. Если у Вас возникнут вопросы, то обращайтесь в мини-форум консультации.
Вам дано линейное неоднородное уравнение второго порядка с постоянными коэффициентами. Общее решение этого уравнения равно сумме общего решения соответствующего однородного уравнения и какого-либо частного решения заданного неоднородного уравнения.
Вычислим сначала общее решение соответствующего однородного уравнения, то есть уравнения
Составим характеристическое уравнение
и, решая его, вычислим корни: Значит, общее решение уравнения -- функцияЧтобы вычислить частное решение заданного дифференциального уравнения, можно воспользоваться тем, что его правая часть
является многочленом третьей степени. Я предлагаю Вам прочитать эту статью, внимательно разобрать примеры и вычислить частное решение самостоятельно. Если у Вас возникнут вопросы, то обращайтесь в мини-форум консультации.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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