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Консультация № 185452
16.02.2012, 18:32
72.84 руб.
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе: Найдите частное решение дифференциального уравнения второго порядка,
удовлетворяющее заданным начальным условиям:
удовлетворяющее заданным начальным условиям:
Обсуждение
16.02.2012, 20:02
общий
это ответ
Здравствуйте, Посетитель - 383833!
Для понижения порядка вводим y как независимую переменную и p(y)=y' как новую функцию. Тогда y''=p'p и получаем уравнение
p'p=18y3
pdp=18y3dy
p2=9y4+Const
(y')2=9y4+Const
Из начального условия при x=1, имем 9=9+Const ---> Const=0, поэтому имеем уравнение
y'=3y2
dy/y2=3dx
-1/y=3x+Const, меняя Const на -Const, получаем
y=1/(Const-3x)
Из начального условия y(1)=1, находим Const=4
Ответ: y=1/(4-3x)
Для понижения порядка вводим y как независимую переменную и p(y)=y' как новую функцию. Тогда y''=p'p и получаем уравнение
p'p=18y3
pdp=18y3dy
p2=9y4+Const
(y')2=9y4+Const
Из начального условия при x=1, имем 9=9+Const ---> Const=0, поэтому имеем уравнение
y'=3y2
dy/y2=3dx
-1/y=3x+Const, меняя Const на -Const, получаем
y=1/(Const-3x)
Из начального условия y(1)=1, находим Const=4
Ответ: y=1/(4-3x)
Форма ответа
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