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Консультация № 160237
11.02.2009, 21:24
0.00 руб.
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Добрый вечер! Помогите пожалуйста решить: проверить, является ли решение дифференциального уравнения .
y'-xy=0
(1+y^2)*dx-xydy=0
y'-cosx=0; y(П/2)=2.
Спс
y'-xy=0
(1+y^2)*dx-xydy=0
y'-cosx=0; y(П/2)=2.
Спс
Обсуждение
Неизвестный
13.02.2009, 13:02
общий
это ответ
Здравствуйте, dmi_5116!
y'-xy=0
dy/dx - xy=0
dy/dx=xy
dy/y=xdx
Int[dy/y]=Int[xdx]
lny=x2/2+C
y=Ce^[x2/2]
(1+y2)*dx-xydy=0
(1+y2)*dx=xydy
dx/x=ydy/(1+y2)
Int[dx/x]=Int[ydy/(1+y2)]
lnCx=1/2*ln(1+y2)
Cx=sqrt(1+y2)
Cx2=1+y2
y=sqrt(Cx2-1)
y'-cosx=0; y(П/2)=2
dy/dx=cosx
dy=cosxdx
y=sinx+C
2=sin(pi/2)+C
2=1+C
C=1
y=sinx+1
y'-xy=0
dy/dx - xy=0
dy/dx=xy
dy/y=xdx
Int[dy/y]=Int[xdx]
lny=x2/2+C
y=Ce^[x2/2]
(1+y2)*dx-xydy=0
(1+y2)*dx=xydy
dx/x=ydy/(1+y2)
Int[dx/x]=Int[ydy/(1+y2)]
lnCx=1/2*ln(1+y2)
Cx=sqrt(1+y2)
Cx2=1+y2
y=sqrt(Cx2-1)
y'-cosx=0; y(П/2)=2
dy/dx=cosx
dy=cosxdx
y=sinx+C
2=sin(pi/2)+C
2=1+C
C=1
y=sinx+1
Форма ответа
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