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Консультация № 179762
22.08.2010, 17:31
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Уважаемые эксперты! Нужна помощь с решением дифференциальных уравнений:
1)2yy’’-3y’=4*(y^2)
2)y’-y/x=x
3)y’’-4y’+8y=(e^2x)+((sinx)^2)
1)2yy’’-3y’=4*(y^2)
2)y’-y/x=x
3)y’’-4y’+8y=(e^2x)+((sinx)^2)
Обсуждение
Неизвестный
22.08.2010, 19:57
общий
02.10.2010, 02:23
это ответ
Здравствуйте, Мазов Сепан Сергеевич!
2) перед нами линейное уравнение, воспользуемся заменой y=uv:
u’v+v’u+uv/x-x=0
u’v+uv/x=0
u’= - u/x
du/u=-dx/x
ln u=-ln Cx
u=1/Cx
тогда v’u-x=0
v’/Cx=x
dv=C*x^2*dx
v=C*x^3/3 + C1
Решено неверно: решением этого линейного дифф. уравнения является y=(x+c)x
2) перед нами линейное уравнение, воспользуемся заменой y=uv:
u’v+v’u+uv/x-x=0
u’v+uv/x=0
u’= - u/x
du/u=-dx/x
ln u=-ln Cx
u=1/Cx
тогда v’u-x=0
v’/Cx=x
dv=C*x^2*dx
v=C*x^3/3 + C1
Решено неверно: решением этого линейного дифф. уравнения является y=(x+c)x
23.08.2010, 09:31
общий
Мазов Сепан Сергеевич:
Подозреваю, что Вы неточно записали первое уравнение. Достаточно просто решается, если вместо 3y' имеется 3(y')^2... А решение третьего уравнения смотрите здесь.
Подозреваю, что Вы неточно записали первое уравнение. Достаточно просто решается, если вместо 3y' имеется 3(y')^2... А решение третьего уравнения смотрите здесь.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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