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Консультация № 160976
20.02.2009, 12:31
0.00 руб.
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1
пожалуйста, помогите найти частные решения следующих дифференциальных уравнений:
2(х+1) dy=ydx при у=2, х=1
dy/dx -2у-4=0 при у=2, х=0
2(х+1) dy=ydx при у=2, х=1
dy/dx -2у-4=0 при у=2, х=0
Обсуждение
Неизвестный
20.02.2009, 13:57
общий
это ответ
Здравствуйте, NESIKA!
1) 2*INT[dy/y]=INT[dx/(x+1)]
2*Ln|y|=Ln|(C^2)*(x+1)|
y^2=(C^2)*(x+1)
y=C*sqrt(x+1)
Подставим начальные условия и решим задачу Коши .
y(1)=2=C*sqrt(1+1) => C=sqrt2
OTBET : Y(x)=sqrt(2x+2) .
2) dy/dx=2*(y+2)
INT[dy/(y+2)]=2*INT[dx]
Ln|y+2|=2x+C
Подставим начальные условия и решим задачу Коши .
{ у=2 , х=0 } => Ln|2+2|=2*0+C => C=Ln4
y+2=4*exp(2x)
OTBET : Y(x)=4*exp(2x)-2 .
1) 2*INT[dy/y]=INT[dx/(x+1)]
2*Ln|y|=Ln|(C^2)*(x+1)|
y^2=(C^2)*(x+1)
y=C*sqrt(x+1)
Подставим начальные условия и решим задачу Коши .
y(1)=2=C*sqrt(1+1) => C=sqrt2
OTBET : Y(x)=sqrt(2x+2) .
2) dy/dx=2*(y+2)
INT[dy/(y+2)]=2*INT[dx]
Ln|y+2|=2x+C
Подставим начальные условия и решим задачу Коши .
{ у=2 , х=0 } => Ln|2+2|=2*0+C => C=Ln4
y+2=4*exp(2x)
OTBET : Y(x)=4*exp(2x)-2 .
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