dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急如题

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dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急如题
dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急
如题

dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急如题
dy/dx=(2y+4)/(x+y-1 )
设Y= y+2 X=x-3 代入：
dY/dX=2Y/(X+Y)
2dX/dY=X/Y+1
设U=X/Y X=YU dX/dY=U+YdU/dY 代入：
2(U+YdU/dY)=U+1
2dU/(1-U)=dY/Y
积分得：-2ln(1-U)+lnC=lnY
Y(1-U)²=C
Y(1-X/Y)²=C
(Y-X)²=CY
或：(y-x+5)²=C(y+2)

u = y+2
u' = 2u/(x+u-3)
dx/du = 1/(du/dx) = x/2u + 1/2 -3 /2u
dx/du = x/2u => dx/x = du/2u => x = 根号(u) +C
dx/du = 1/2 => x= 0.5u +C
dx/du =-3/2u => x = -1.5 ln|u|
所以x = 根号u + 0.5u -1.5 ln|u| +C
x= 根号(y+2) +0.5 y -1.5 ln|y+2| +C

x=y²-y/y+4

(x^2)dy+（y^2)dx=dx-dy 已知x=y^2-4y,求dy/dx dy/dx=x(1+y^2)/y通解 dy/dx,y=(1+x+x^2)e^x dy/dx=1+1/(x-y) dy/dx=1-cos(y-x) dy/dx=x(1-y) dy/dx = 1/x-y 微分方程 dy/dx=(-2x)/y dy/dx=x+y dy/dx=(e^x+x)(1+y^2)通解 反函数的二阶导数疑问设dy/dx=y',则dx/dy=1/y',应视为y的函数则d2x/dy2=d(dx/dy)/dy（定义）=d(1/(dy/dx)) / dy=d(1/(dy/dx))/dx * dx/dy（复合函数求导,x是中间变量）=-y''/(y')^2 * (1/y')=-y''/(y')^3d(1/(dy/dx))/dx * dx/dy y=[sin(x^4)]^2,则dy/dx=?,dy^2/dx^2=?,dy/d(x^2)=? dy/dx 3x^2+4y^3-2x-5y+1=0 求解微分方程dy/dx=(x+y-1)/(x+4y+2) 求方程(2x+y-4)dx+(x+y-1)dy=0的通解. 设x^2+y^2=4,求dy/dx x=sint+1 y=2cos3t dy/dx