dy/dx=[y^2 - x^2]/2xy 求通解dy/dx=[y^2 - x^2]/2xy 求通解

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dy/dx=[y^2 - x^2]/2xy 求通解dy/dx=[y^2 - x^2]/2xy 求通解
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dy/dx=[y^2 - x^2]/2xy 求通解dy/dx=[y^2 - x^2]/2xy 求通解
dy/dx=[y^2 - x^2]/2xy 求通解
dy/dx=[y^2 - x^2]/2xy 求通解

dy/dx=[y^2 - x^2]/2xy 求通解dy/dx=[y^2 - x^2]/2xy 求通解
设y=tx,则dy=xdt+tdx,
∴dy/dx=xdt/dx+t,原方程变为
xdt/dx+t=(1/2)(t-1/t),
∴xdt/dx=(-1/2)(t+1/t),
∴2tdt/(t^2+1)=-dx/x,
积分得ln(t^2+1)=-lnx+lnc,
∴t^2+1=c/x,
代入假设得x^2+y^2=cx.

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