求解下列初值问题 5
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令：v=y/x,y=xv,dy=vdx+xdv
dy/dx = -(y^2-2xy)/x^2
(vdx+xdv)/dx = 2v - v^2
v+xdv/dx = 2v - v^2
xdv/dx = v - v^2
dv/[v(1 - v)] = dx/x
∫dv/[v(1 - v)] = ∫dx/x
∫dv/v + ∫dv/(1 - v)] = ∫dx/x
lnv - ln(1-v) = lnx
ln(v/(1-v))=lnx+lnc
v/(1-v)=cx
(y/x)/(1-(y/x))=cx
y/(x-y)=cx
y=cx(x-y)
dy/dx = -(y^2-2xy)/x^2
(vdx+xdv)/dx = 2v - v^2
v+xdv/dx = 2v - v^2
xdv/dx = v - v^2
dv/[v(1 - v)] = dx/x
∫dv/[v(1 - v)] = ∫dx/x
∫dv/v + ∫dv/(1 - v)] = ∫dx/x
lnv - ln(1-v) = lnx
ln(v/(1-v))=lnx+lnc
v/(1-v)=cx
(y/x)/(1-(y/x))=cx
y/(x-y)=cx
y=cx(x-y)
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