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Консультация № 184225
15.10.2011, 02:36
51.74 руб.
15.10.2011, 15:31
0
2
2
Здравствуйте, уважаемые эксперты! Прошу вас помогите разобраться с дифференциальными уравнениями:
С утра сдавать,а идей никаких:(((
С утра сдавать,а идей никаких:(((
Обсуждение
15.10.2011, 08:18
общий
это ответ
Здравствуйте, Ольга Никанова!
С уважением.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
15.10.2011, 09:20
общий
это ответ
Здравствуйте, Ольга Никанова!
4) Решаем уравнение относительно y'
y'=(4x-2)y/x2+2[$8730$]y (уравнение Бернулли)
делим уравнение на 2[$8730$]y и обозначаем z=[$8730$]y
z'=(2x-1)z/x2+2 (линейное уравнение)
сначала решаем однородное z'=(2x-1)z/x2
dz/z=(2x-1)dx/x2
ln|z|=2ln|x|+(1/x)+const
z=Cx2e1/x
затем применяем метод вариации: z=C(x)x2e1/x, получаем
C'(x)=(2/x2)e-1/x
C(x)=2e-1/x+C
таким образом z=2x2+Cx2e1/x
Ответ:
y=(2x2+Cx2e1/x)2, y=0
(y=0 потеряно при делении на 2[$8730$]y)
4) Решаем уравнение относительно y'
y'=(4x-2)y/x2+2[$8730$]y (уравнение Бернулли)
делим уравнение на 2[$8730$]y и обозначаем z=[$8730$]y
z'=(2x-1)z/x2+2 (линейное уравнение)
сначала решаем однородное z'=(2x-1)z/x2
dz/z=(2x-1)dx/x2
ln|z|=2ln|x|+(1/x)+const
z=Cx2e1/x
затем применяем метод вариации: z=C(x)x2e1/x, получаем
C'(x)=(2/x2)e-1/x
C(x)=2e-1/x+C
таким образом z=2x2+Cx2e1/x
Ответ:
y=(2x2+Cx2e1/x)2, y=0
(y=0 потеряно при делении на 2[$8730$]y)
Форма ответа
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