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Консультация № 195721
26.05.2019, 15:49
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти первые пять членов разложения решения дифференциального уравнения в степенной ряд.
y'=3cosx-xy²
y(1)=0
Найти первые пять членов разложения решения дифференциального уравнения в степенной ряд.
y'=3cosx-xy²
y(1)=0
Обсуждение
30.05.2019, 09:08
общий
это ответ
Здравствуйте, 666asul666!
Согласно [1, с. 140 -- 141], вычислим решение уравнения методом последовательного дифференцирования в виде ряда Тейлора
взяв первые пять членов, отличных от нуля.
1)
2)
3)
4)
5)
Подставляя значения производных в формулу (1), получим
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: в 2 ч. Ч. 2. -- М.: Айрис-пресс, 2007. -- 256 с.
Разумеется, проверка предложенного мной решения, в котором легко ошибиться, остаётся за Вами. Если Вам нужно, подставьте в формулы значения
и 
и выполните нужные преобразования, чтобы получить численные значения коэффициентов разложения в явном виде.
Согласно [1, с. 140 -- 141], вычислим решение уравнения методом последовательного дифференцирования в виде ряда Тейлора
взяв первые пять членов, отличных от нуля.
1)
2)
3)
4)
5)
Подставляя значения производных в формулу (1), получим
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: в 2 ч. Ч. 2. -- М.: Айрис-пресс, 2007. -- 256 с.
Разумеется, проверка предложенного мной решения, в котором легко ошибиться, остаётся за Вами. Если Вам нужно, подставьте в формулы значения
и и выполните нужные преобразования, чтобы получить численные значения коэффициентов разложения в явном виде.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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