求y'=y/(y-x)

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求y''=y/(y-x)求y''=y/(y-x)求y''=y/(y-x)∵令y=xt,则y''=xt''+t代入原方程,得xt''+t=t/(t-1)==>xt''=(2t-t^2)/(t-1)==>(t-1)dt

求y'=y/(y-x)
求y'=y/(y-x)

求y'=y/(y-x)
∵令y=xt,则y'=xt'+t
代入原方程,得xt'+t=t/(t-1)
==>xt'=(2t-t^2)/(t-1)
==>(t-1)dt/(2t-t^2)=dx/x
==>2dx/x+[1/t+1/(t-2)]dt=0
==>2ln│x│+ln│t│+ln│t-2│=ln│C│ (C是常数)
==>x^2t(t-2)=C
==>x^2(y/x)(y/x-2)=C
==>y(y-2x)=C
∴原方程的通解是y(y-2x)=C.

反过来求解，dx/dy=1-x/y，然后自己再想办法吧，呵呵

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