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Консультация № 177576
31.03.2010, 19:21
42.84 руб.
0
4
1
1) Найти общее решение дифференциального уравнения:
y'=(x+y)/(x-y)
2) Найти решение задачи Коши:
xy'=(x^5*y^2-2y)
y(1)=1
y'=(x+y)/(x-y)
2) Найти решение задачи Коши:
xy'=(x^5*y^2-2y)
y(1)=1
Обсуждение
Неизвестный
02.04.2010, 20:03
общий
star9491:
Уважаемый Эксперт!
Спасибо за решение задач. Не могли бы вы подсказать, как в первой задаче из формулы arctg(y/x)-1/2ln(x^2+y^2)/x^2=ln/x/+const вычисляется x?
Заранее спасибо!
Уважаемый Эксперт!
Спасибо за решение задач. Не могли бы вы подсказать, как в первой задаче из формулы arctg(y/x)-1/2ln(x^2+y^2)/x^2=ln/x/+const вычисляется x?
Заранее спасибо!
02.04.2010, 20:25
общий
Матвеев Денис Александрович:
После потенцирования получаем
e^(arctg(y/x))e^(-1/2ln[(x2+y2)/x2])=e^(ln|x|)e^(const)
Далее
e^(-1/2ln[(x2+y2)/x2)])=e^(ln[(x^2+y^2)/x^2)]-1/2)=[(x2+y2)/x2)]-1/2=|x|/[$8730$](x2+y2)
e^(ln|x|)=|x|
e^(const)=const (другая)
поэтому
e^(arctg(y/x))|x|/[$8730$](x2+y2)=const|x|
или
e^(arctg(y/x))/[$8730$](x2+y2)=const
После потенцирования получаем
e^(arctg(y/x))e^(-1/2ln[(x2+y2)/x2])=e^(ln|x|)e^(const)
Далее
e^(-1/2ln[(x2+y2)/x2)])=e^(ln[(x^2+y^2)/x^2)]-1/2)=[(x2+y2)/x2)]-1/2=|x|/[$8730$](x2+y2)
e^(ln|x|)=|x|
e^(const)=const (другая)
поэтому
e^(arctg(y/x))|x|/[$8730$](x2+y2)=const|x|
или
e^(arctg(y/x))/[$8730$](x2+y2)=const
Форма ответа
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