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Консультация № 179393
Обсуждение
Неизвестный
05.07.2010, 01:03
общий
26.07.2010, 10:05
это ответ
Здравствуйте, Арефин Сергей Викторович.
приведем к виду:
(y^2/(1-y))dy=-(x^2/(1+x))dx
интегрируем,
делаем замену в первом интеграле
y^2=t, во втором аналагочино x^2=t
получаем:
-1/2*y^2-y-ln(1-y)+C=-1/2*x^2+x-ln(1+x)
Ответ: C=-1/2*x^2+x-ln(1+x)+1/2*y^2+y+ln(1-y)
приведем к виду:
(y^2/(1-y))dy=-(x^2/(1+x))dx
интегрируем,
делаем замену в первом интеграле
y^2=t, во втором аналагочино x^2=t
получаем:
-1/2*y^2-y-ln(1-y)+C=-1/2*x^2+x-ln(1+x)
Ответ: C=-1/2*x^2+x-ln(1+x)+1/2*y^2+y+ln(1-y)
06.07.2010, 17:54
общий
это ответ
Здравствуйте, Арефин Сергей Викторович.
y^2(1+x)y'=x^2(y-1)
dy/dx*y^2(1+x)=x^2(y-1)
y^2(1+x)dy=x^2(y-1)dx
Интегрируем обе части уравнения:
y^2/(y-1)dy=x^2/(1+x)dx
Получаем:
1/2y^2+y+ln(y+1)=1/2x^2-x+ln(1+x)+C
Общее решение уравнения
C=1/2y^2+y+ln(y+1)-1/2x^2+x-ln(1+x)
Думаю правильнее так записать.
y^2(1+x)y'=x^2(y-1)
dy/dx*y^2(1+x)=x^2(y-1)
y^2(1+x)dy=x^2(y-1)dx
Интегрируем обе части уравнения:
y^2/(y-1)dy=x^2/(1+x)dx
Получаем:
1/2y^2+y+ln(y+1)=1/2x^2-x+ln(1+x)+C
Общее решение уравнения
C=1/2y^2+y+ln(y+1)-1/2x^2+x-ln(1+x)
Думаю правильнее так записать.
Форма ответа
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