y导=(y/x)—(y^2/x^2)的通解?

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y导=(y/x)—(y^2/x^2)的通解?

y导=(y/x)—(y^2/x^2)的通解?
y导=(y/x)—(y^2/x^2)的通解?

y导=(y/x)—(y^2/x^2)的通解?
令t=y/x
y=tx
dy/dx=t+x*dt/dx
原式可化为 t+x*dt/dx=t-t^2
x*dt/dx=-t^2
dt/(-t^2)=dx/x 两边求积分可得
1/t=lnx+c
t=1/(lnx+c)
故原方程的通解为
y=tx=x/(lnx+c)
^.^

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