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Консультация № 190715
16.03.2017, 17:20
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
1) y-xy'=1+(x^2)y' ;
2)(x-y)dx+(x+y)dy=0 ;
3)xy'-2y=2x^4 ;
4)y'=(y^4) cos(x) + y tg(x).
1) y-xy'=1+(x^2)y' ;
2)(x-y)dx+(x+y)dy=0 ;
3)xy'-2y=2x^4 ;
4)y'=(y^4) cos(x) + y tg(x).
Обсуждение
17.03.2017, 05:31
общий
это ответ
Здравствуйте, anka.gorelkina!
1) Используем разделение переменных:
Интегрируем:
2) Введём переменную p = y/x, тогда y = px и dy = p dx + x dp. Подставляем в исходное уравнение:
Разделяем переменные:
и интегрируем
или после подстановки p = y/x:
3) Сокращаем на x[sup]3[/sup]:
Воспользуемся формулой для производной произведения:
Интегрируем:
4) Сокращаем на y[sup]4[/sup]cos[sup]3[/sup]x/3:
Воспользуемся формулой для производной произведения:
Интегрируем:
1) Используем разделение переменных:
Интегрируем:
2) Введём переменную p = y/x, тогда y = px и dy = p dx + x dp. Подставляем в исходное уравнение:
Разделяем переменные:
и интегрируем
или после подстановки p = y/x:
3) Сокращаем на x[sup]3[/sup]:
Воспользуемся формулой для производной произведения:
Интегрируем:
4) Сокращаем на y[sup]4[/sup]cos[sup]3[/sup]x/3:
Воспользуемся формулой для производной произведения:
Интегрируем:
Форма ответа
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