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Консультация № 170057
Обсуждение
Неизвестный
01.07.2009, 12:35
общий
это ответ
Здравствуйте, Якупов Ринат Ильдарович.
Как я понял диф. уравнение имеет вид:
yy'=(1-2x)/y
Тогда это уравнение с разделяющимися переменными:
y*(dy/dx) = (1-2x)/y /*(y*dx)
(y^2)dy = (1-2x)dx
Интегрируем:
I(y^2)dy = I(1-2x)dx, где I - знак интеграла
(y^3)/3 + C1 = x - (x^2) + C2, где C1, C2 - константы
(y^3) - 3x + 3(x^2) = C, где С - константа
Это и будет решением, то есть общим интегралом уравнения
Как я понял диф. уравнение имеет вид:
yy'=(1-2x)/y
Тогда это уравнение с разделяющимися переменными:
y*(dy/dx) = (1-2x)/y /*(y*dx)
(y^2)dy = (1-2x)dx
Интегрируем:
I(y^2)dy = I(1-2x)dx, где I - знак интеграла
(y^3)/3 + C1 = x - (x^2) + C2, где C1, C2 - константы
(y^3) - 3x + 3(x^2) = C, где С - константа
Это и будет решением, то есть общим интегралом уравнения
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