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Полная версия: y'' * y^3 + 36 = 0, y(0) = 3, y'(0) = 2 > Дифференциальные уравнения
Образовательный студенческий форум > Высшая математика > Дифференциальные уравнения
kirill
не знаю как решить y"*y^3+36=0, y(0)=3, y'(0)=2, помогите пожалуйста
venja
Уравнеие не содержит х. Может быть сведено к уравнению 1 порядка
заменой y'(x)=z(y(x)), т.е., короче, y'=z, где z=z(y) искомая вспомог. ф-я. Тогда y''=z*z'. Подставить.
kirill
Цитата(venja @ 27.5.2007, 7:07) *

Уравнеие не содержит х. Может быть сведено к уравнению 1 порядка
заменой y'(x)=z(y(x)), т.е., короче, y'=z, где z=z(y) искомая вспомог. ф-я. Тогда y''=z*z'. Подставить.


to venja БОЛЬШОЕ СПАСИБО! Молодец - я-то парился, спс.
newbe
y''*y*y*y - 3 = 0
kak reshit?
Esli,
y'=z, z=z(y), y''=z*z'
resenie:
y*y*y*z*z' - 3 = 0 / :z
y*y*y*z'-3/z=0
y*y*y*dz/dy-3/z=0 /*dy
y*y*y*dz-(3/z)*dy=0 /*z :y*y*y
z*dz=(3/y*y*y)*dy=0
tak pravilno?
Dalee u menya poluchaetsya
z*z*y*y+3=C1
z*z=-3/y*y+C1/y*y
I esli moi vichisleniya verni
To kakoi otvet okonchatelnii, esli net nachalnih usloviy?
wils
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wils
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