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【1】求下列方程所确定的dy/dx
[1] y^2-2xy+9=0
2ydy-2ydx-2xdy=0
(y-x)dy=ydx
dy/dx=y/(y-x)
[2] x^3+y^3-3axy=0
3x^2dx+3y^2dy-3aydx-3axdy=0
(3y^2-ax)dy=(ay-x^2)dx
dy/dx=(ay-x^)/(3y^2-ax)
[3]xy=e^[x+y]
ydx+xdy=e^(x+y) *(dx+dy)
[x-e^(x+y)]dy=[e^(x+y)-y]dx
dy/dx=[e^(x+y)-y]/ [x-e^(x+y)]
[4]y=1-xe^y
[1] y^2-2xy+9=0
2ydy-2ydx-2xdy=0
(y-x)dy=ydx
dy/dx=y/(y-x)
[2] x^3+y^3-3axy=0
3x^2dx+3y^2dy-3aydx-3axdy=0
(3y^2-ax)dy=(ay-x^2)dx
dy/dx=(ay-x^)/(3y^2-ax)
[3]xy=e^[x+y]
ydx+xdy=e^(x+y) *(dx+dy)
[x-e^(x+y)]dy=[e^(x+y)-y]dx
dy/dx=[e^(x+y)-y]/ [x-e^(x+y)]
[4]y=1-xe^y
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