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e^(x/y) = xy
x/y = ln(xy) = lnx+lny
(y+xy')/y² = 1/x+1/y*y'
y+xy' = y²/x+yy'
(x-y)y' = y²/x-y
y' = (y²/x-y)/(x-y)
dy = [(y²/x-y)/(x-y)] dx
x/y = ln(xy) = lnx+lny
(y+xy')/y² = 1/x+1/y*y'
y+xy' = y²/x+yy'
(x-y)y' = y²/x-y
y' = (y²/x-y)/(x-y)
dy = [(y²/x-y)/(x-y)] dx
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两边全微分
e^(x/y)*(1/y)dx-e^(x/y)*(x/y^2)dy=ydx+xdy
(x+e^(x/y)*(x/y^2))dy=(e^(x/y)*(1/y)-y)dx
dy=(e^(x/y)*(1/y)-y)/(x+e^(x/y)*(x/y^2))*dx=(y/x)(e^(x/y)-y^2)/(e^(x/y)+y^2) dx=(y/x)(x-y)/(x+y)*dx
e^(x/y)*(1/y)dx-e^(x/y)*(x/y^2)dy=ydx+xdy
(x+e^(x/y)*(x/y^2))dy=(e^(x/y)*(1/y)-y)dx
dy=(e^(x/y)*(1/y)-y)/(x+e^(x/y)*(x/y^2))*dx=(y/x)(e^(x/y)-y^2)/(e^(x/y)+y^2) dx=(y/x)(x-y)/(x+y)*dx
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